Deck 3: Polynomials

Question 1

Raise the monomial to the indicated power. $\left( a b ^ { 6 } c ^ { 3 } \right) ^ { 2 }$

A) $a ^ { 2 } b ^ { 8 } c ^ { 5 }$
B) $a ^ { 3 } b ^ { 12 } c ^ { 5 }$
C) $a ^ { 3 } b ^ { 8 } c ^ { 5 }$
D) $a ^ { 2 } b ^ { 12 } c ^ { 6 }$
E) $a ^ { 3 } b ^ { 8 } c ^ { 6 }$

Answer 1

$a ^ { 2 } b ^ { 12 } c ^ { 6 }$

Question 2

Find the product. $$\left( 4 s ^ { 6 } z ^ { 6 } \right) \left( 3 s ^ { 4 } z ^ { 3 } \right)$$

A) $14 s ^ { 11 } z ^ { 10 }$
B) $12 s ^ { 10 } z ^ { 9 }$
C) $12 s ^ { 2 } z ^ { 3 }$
D) $12 s ^ { 24 } z ^ { 18 }$
E) $7 s ^ { 10 } z ^ { 9 }$

Answer 2

$12 s ^ { 10 } z ^ { 9 }$

Question 3

Simplify the expression. $$2 \left( x ^ { 2 } - 7 x - 4 \right) - 3 \left( x ^ { 2 } - 7 x - 4 \right) + 9 \left( x ^ { 2 } - 7 x - 4 \right)$$

A) $8 x ^ { 2 } - 98 x - 56$
B) $8 x ^ { 2 } - 98 x - 32$
C) $8 x ^ { 2 } - 56 x - 32$
D) $8 x ^ { 2 } - 56 x - 56$
E)none of these

Answer 3

$8 x ^ { 2 } - 56 x - 32$

Question 4

Simplify the expression. $$- 4 x y ^ { 2 } ( 3 x + 2 y + 5 z ) - 2 x \left( x y ^ { 2 } - 4 y ^ { 2 } z \right) - 2 y \left( 8 x y ^ { 2 } - 1 \right)$$

A) $- 10 x ^ { 2 } y ^ { 2 } - 28 x y ^ { 2 } z - 24 x y ^ { 3 } + 2 y$
B) $- 14 x ^ { 2 } y ^ { 2 } - 28 x y ^ { 2 } z + 24 x y ^ { 3 } + 2 y$
C) $- 14 x ^ { 2 } y ^ { 2 } - 12 x y ^ { 2 } z - 24 x y ^ { 3 } + 2 y$
D) $- 14 x ^ { 2 } y ^ { 2 } - 28 x y ^ { 2 } z - 24 x y ^ { 3 } + 2 y$
E)none of these

Question 5

Simplify the expression. $$\left( 20 z ^ { 2 } + 10 z + 6 \right) + \left( 9 z ^ { 2 } + 9 z + 1 \right)$$

A) $29 z ^ { 2 } + 10 z + 7$
B) $29 z ^ { 2 } + 19 z + 7$
C) $29 z ^ { 2 } + 19 z$
D) $20 z ^ { 2 } + 19 z + 7$
E)none of these

Question 6

Raise the monomial to the indicated power. $\left( 5 x y ^ { 5 } \right) ^ { 3 }$

A) $125 x ^ { 3 } y ^ { 8 }$
B) $125 x ^ { 4 } y ^ { 8 }$
C) $125 x ^ { 3 } y ^ { 15 }$
D) $15 x ^ { 4 } y ^ { 8 }$
E) $15 x ^ { 3 } y ^ { 8 }$

Question 7

Find a polynomial that represents the total surface area of the right circular cylinder, and use that polynomial to determine the total surface area of the following right circular cylinder that has a base with a radius of 4. Use 3.14 for $\pi$ , and express the answers to the nearest tenth. Let h = 7.

A)A = 176.1
B)A = 138.2
C)A = 326.1
D)A = 276.3
E)A = 226.1

Question 8

Raise the monomial to the indicated power. $- ( 5 a b ) ^ { 3 }$

A) $- 125 a ^ { 4 } b ^ { 4 }$
B) $- 15 a ^ { 4 } b ^ { 4 }$
C) $15 a ^ { 3 } b ^ { 3 }$
D) $- 125 a ^ { 3 } b ^ { 3 }$
E) $125 a ^ { 4 } b ^ { 4 }$

Question 9

Determine the degree of the given polynomial. $$3 x ^ { 3 } y ^ { 2 } - 9 x ^ { 3 } y ^ { 3 }$$

A)5
B)0
C)3
D)6
E)1

Question 10

Subtract the bottom polynomial from the top polynomial. $$\begin{array} { c } - 5 y ^ { 3 } + 4 y ^ { 2 } - 11 y + 5 \\- 2 y ^ { 3 } - 14 y ^ { 2 } + 17 y - 34\\\hline\end{array}$$

A) $- 5 y ^ { 3 } - 13 y ^ { 2 } + 21 y - 40$
B) $3 y ^ { 3 } + 18 y ^ { 2 } - 28 y - 39$
C) $- 3 y ^ { 3 } + 18 y ^ { 2 } - 28 y + 39$
D) $- 3 y ^ { 3 } - 18 y ^ { 2 } + 28 y - 41$
E) $- 7 y ^ { 3 } + 10 y ^ { 2 } + 28 y + 36$

Question 11

Find the product. $$\left( y a ^ { 3 } \right) \left( 2 y ^ { 5 } a ^ { 6 } \right) \left( 3 y ^ { 2 } a \right)$$

A) $5 y ^ { 8 } a ^ { 10 }$
B) $6 y ^ { 8 } a ^ { 10 }$
C) $6 y ^ { 12 } a ^ { 24 }$
D) $6 y ^ { 4 } a ^ { 2 }$
E)none of these

Question 12

Simplify the expression. 3 y ( xy + y )- 9 y ²( x - 2 + 5 y )+ 2( y ³ + y ²)

A)- 6 xy ² + 21 y ² + 20 y ³
B)- 6 xy ² + 23 y ² - 43 y ³
C)12 xy ² + 21 y ² - 43 y ³
D)6 xy ² + 21 y ² - 20 y ³
E)none of these

Question 13

The area of a triangular sheet of paper is 11 square inches. One side of the triangle is 5 inches more than three times the length of the altitude to that side. Find the length of that side and the altitude to the side.

A)an altitude of 11 inches, a side of 21 inches long
B)an altitude of 2 inches, a side of 11 inches long
C)an altitude of 1 inches, a side of 11 inches long
D)an altitude of 11 inches, a side of 2 inches long
E)none of these

Question 14

Find the product. $\left( 4 x ^ { 3 } \right) \left( 3 x ^ { 5 } \right)$

A) $12 x ^ { 8 }$
B) $12 x ^ { 15 }$
C) $7 x ^ { 8 }$
D) $7 x ^ { 15 }$
E)none of these

Question 15

Find the quotient. $\frac { - 20 x ^ { 5 } y ^ { 9 } z ^ { 9 } } { x ^ { 2 } y z ^ { 3 } }$

A) $- 20 x ^ { 7 } y ^ { 8 } z ^ { 6 }$
B) $- 20 x ^ { 7 } y ^ { 9 } z ^ { 12 }$
C) $- 20 x ^ { 7 } y ^ { 10 } z ^ { 12 }$
D) $- 20 x ^ { 3 } y ^ { 8 } z ^ { 6 }$
E) $- 20 x ^ { 3 } y ^ { 8 } z ^ { 12 }$

Question 16

Simplify the expression. $$( 5 x + 5 ) + ( 9 x - 3 )$$

A) $14 x + 2$
B) $14 x - 2$
C) $14 x + 5$
D) $5 x + 2$
E)none of these

Question 17

Determine the degree of the given polynomial. -5

A)0
B)9
C)5
D)7
E)4

Question 18

The Ortegas have an apple orchard that contains 75 trees. The number of trees in each row is 5 more than twice the number of rows. Find the number of rows and the number of trees per row. __________ rows __________ trees per row

Question 19

Find the quotient. $$\frac { 15 x ^ { 5 } y ^ { 5 } } { 3 x y ^ { 3 } }$$

A) $x ^ { 5 } y ^ { 2 }$
B) $5 x ^ { 5 } y ^ { 4 }$
C) $5 x ^ { 5 } y ^ { 2 }$
D) $5 x ^ { 4 } y ^ { 2 }$
E) $5 x ^ { 4 } y ^ { 4 }$

Question 20

Determine the degree of the given polynomial. 3 xy + 7 y

A)0
B)2
C)11
D)3
E)1

Question 21

Find the product. $$\frac { 8 } { 3 } a ^ { 2 } b ( 6 a - 8 b )$$

A) $\frac { 16 } { 3 } a ^ { 2 } b - \frac { 64 } { 3 } a ^ { 2 } b ^ { 2 }$
B) $\frac { 16 } { 3 } a ^ { 3 } b + \frac { 64 } { 3 } a ^ { 2 } b ^ { 2 }$
C) $16 a ^ { 3 } b - \frac { 64 } { 3 } a ^ { 2 } b ^ { 2 }$
D) $16 a ^ { 3 } b - \frac { 56 } { 3 } a b ^ { 2 }$
E) $16 a ^ { 2 } b + \frac { 64 } { 3 } a ^ { 2 } b ^ { 2 }$

Question 22

Find the product. $( 3 z - 3 t ) ^ { 2 }$

A) $9 z ^ { 2 } - 3 z - 3 t + 9 t ^ { 2 }$
B) $9 z ^ { 2 } - 9 t ^ { 2 }$
C) $9 z ^ { 2 } + 9 t ^ { 2 }$
D) $9 z ^ { 2 } - 18 z t + 9 t ^ { 2 }$
E) $9 z ^ { 2 } - 9 z t + 9 t ^ { 2 }$

Question 23

Find the product.

Question 24

Factor the composite number 21 into the product of prime numbers. For example: 30 = 2 * 3 * 5.

A) $7 \cdot 3$
B) $21 \cdot 1$
C) $3 + 18$
D) $19 + 2$
E) $1 \cdot 21$

Question 25

Factor completely. $42 x ^ { 3 } y ^ { 4 } - 30 x ^ { 4 } y ^ { 3 }$

A) $6 x ^ { 3 } y ^ { 3 } ( 7 y - 5 x )$
B) $6 y ^ { 3 } \left( 7 x ^ { 3 } y - 5 x ^ { 4 } \right)$
C) $6 x ^ { 3 } \left( 7 y ^ { 4 } - 5 x y ^ { 3 } \right)$
D) $6 \left( 7 y ^ { 4 } y - 5 x ^ { 4 } \right)$
E) $x ^ { 3 } y ^ { 3 } ( 42 y - 30 x )$

Question 26

Find (9 x + 9)³ . Don't forget that (9 x + 9)³ means (9 x + 9)(9 x + 9)(9 x + 9).

A)729 x ³ + 729 x ² + 2,187 x + 729
B)729 x ³ + 2,187 x ² + 2,187 x + 81
C)729 x ³ + 2,187 x ² + 729 x + 729
D)729 x ³ + 243 x ² + 2,187 x + 729
E)729 x ³ + 2,187 x ² + 2,187 x + 729

Question 27

Classify the number as prime or composite. 19

A)Prime
B)Composite

Question 28

Find the product. $$\left( - 3 a ^ { 2 } b \right) \left( - 3 a ^ { 3 } b ^ { 2 } \right) ( 6 a - 7 b )$$

A) $21 a ^ { 5 } b ^ { 4 } - 18 a ^ { 6 } b ^ { 3 }$
B) $54 a ^ { 5 } b ^ { 3 } + 42 a ^ { 5 } b ^ { 4 }$
C) $54 a ^ { 6 } b ^ { 3 } - 63 a ^ { 5 } b ^ { 4 }$
D) $63 a ^ { 5 } b ^ { 4 } - 54 a ^ { 6 } b ^ { 3 }$
E) $18 a ^ { 6 } b ^ { 3 } - 21 a ^ { 5 } b ^ { 4 }$

Question 29

Find the quotient. $\frac { - 20 a b c ^ { 7 } } { 20 b c }$

A) $- a b c ^ { 8 }$
B) $- a c ^ { 6 }$
C) $- a b c ^ { 6 }$
D) $- a c ^ { 8 }$
E) $- a c ^ { 7 }$

Question 30

Factor completely. $6 x ^ { 2 } + 26 x$

A) $2 \left( 3 x ^ { 2 } + 13 x \right)$
B) $3 \left( 2 x ^ { 2 } \right) + 13 ( 2 x )$
C) $3 x ( 2 x ) + 13 ( 2 x )$
D) $x ( 6 x + 26 )$
E) $2 x ( 3 x + 13 )$

Question 31

Find the indicated product. (3 x - 6) ³

A)27 x ³ - 162 x ² + 324 x - 6
B)27 x ³ - 162 x ² - 54 x + 6
C)27 x ³ - 162 x ² + 324 x - 216
D)27 x ³ + 162 x ² - 324 x + 216
E)27 x ³ - 324 x ² + 162 x - 216

Question 32

Find a polynomial that represents the volume of the rectangular solid, where a = 6 x , b = 3 x , c = 4 x .

A)V ( x )= 72 x ³
B)V ( x )= 22 x ³
C)V ( x )= 13 x ³
D)V ( x )= 18 x ³
E)V ( x )= 14 x ³

Question 33

Find the product. $( 7 z + 1 ) ( 7 z - 1 )$

A) $49 z ^ { 2 } - 1$
B) $49 z ^ { 2 } - 14 z - 1$
C) $49 z ^ { 2 } + 1$
D) $14 z ^ { 2 } - 1$
E) $14 z ^ { 2 } + 1$

Question 34

Find the product. $$( y + 4 ) ( y - 4 )$$

A) $y ^ { 2 } - 19$
B) $y ^ { 2 } - 20$
C) $y ^ { 2 } - 16$
D) $y ^ { 2 } - 17$
E) $y ^ { 2 } - 18$

Question 35

Find the indicated product. ( x + 3) ³

A)x ³ + 9 x ² + 27 x + 27
B)x ³ + 27 x ² + 9 x + 27
C)x ³ + 3 x ² + 9 x + 27
D)x ³ + 9 x ² + 9 x + 3
E)x ³ + 9 x ² + 27 x + 9

Question 36

Find the product. $( 5 s + z ) ^ { 2 }$

A) $25 s ^ { 2 } + 10 s z + z ^ { 2 }$
B) $23 s ^ { 2 } + 14 s z + z ^ { 2 }$
C) $29 s ^ { 2 } + 16 s z + z ^ { 2 }$
D) $32 s ^ { 2 } + 13 s z + z ^ { 2 }$
E) $26 s ^ { 2 } + 15 s z + z ^ { 2 }$

Question 37

Factor the composite number $66$ into the product of prime numbers. For example: 30 = 2 * 3 * 5.

A) $1 \cdot 3 \cdot 11$
B) $2 \cdot 33$
C) $1 \cdot 6 \cdot 11$
D) $2 \cdot 3 \cdot 11$
E) $3 \cdot 1.22$

Question 38

Find the product. $$\left( a ^ { 4 n } + t ^ { 4 n } \right) \left( a ^ { 4 n } - t ^ { 4 n } \right)$$

A) $a ^ { 8 n } - t ^ { 4 n }$
B) $a ^ { 8 n } + t ^ { 8 n }$
C) $a ^ { 4 n } - t ^ { 8 n }$
D) $t ^ { 8 n } - a ^ { 8 n }$
E) $a ^ { 8 n } - t ^ { 8 n }$

Question 39

Find the product.

Question 40

The owners of the rectangular swimming pool in the illustration want to surround the pool with a crushed-stone border of uniform width. They have enough stone to cover 68 square meters. How wide should they make the border? ( Hint : The area of the larger rectangle minus the area of the smaller is the area of the border.)

A)1.5 m
B)3.5 m
C)1 m
D)2.5 m
E)0.5 m

Question 41

Solve the equation. $x ^ { 3 } + 7 x ^ { 2 } = x ^ { 2 } - 9 x$

A) $x = 3,0$
B) $x = - 3$
C) $x = - 3,0$
D) $x = - 3,3,0$
E) $x = 3$

Question 42

Factor by grouping. $$3 x ^ { 2 } + 21 x - 7 x - 49$$

A) $( 3 x - 7 ) ( x + 7 )$
B) $3 x ^ { 2 } + 21 x - 7 ( x + 7 )$
C) $3 x ( x + 7 ) - 7 ( x + 7 )$
D) $3 x ( x + 7 ) - 7 x + 49$
E) $( 3 x - 7 ) ( x - 49 )$

Question 43

Factor completely. $45 x ^ { 7 } - 7 x ^ { 9 } + 10 x ^ { 10 }$

A) $45 x ^ { 7 } - x ^ { 9 } ( 7 + 10 x )$
B) $x ^ { 7 } \left( 45 - 7 x ^ { 2 } \right) + 10 x ^ { 10 }$
C) $x \left( 45 - 7 x ^ { 8 } + 10 x ^ { 9 } \right)$
D) $x ^ { 7 } \left( 45 + 10 x ^ { 3 } \right) - 7 x ^ { 9 }$
E) $x ^ { 7 } \left( 45 - 7 x ^ { 2 } + 10 x ^ { 3 } \right)$

Question 44

An object has been thrown straight up into the air. The formula $h = v t - 16 t ^ { 2 }$ gives the height h of the object above the ground after t seconds, when it is thrown upward with an initial velocity v . After how many seconds will an object hit the ground if it is thrown with a velocity of 112 feet per second?

A) $t = 18$ sec
B) $t = 23$ sec
C) $t = 6$ sec
D) $t = 20$ sec
E) $t = 7$ sec

Question 45

The combined area of two squares is 153 square meters. The sides of the larger square are 4 times as long as the sides of the smaller square. Find the dimensions of each of the squares.

A)Dimensions of the smaller square are 4 by 4 meters, dimensions of the larger square are 16 by 16 meters.
B)Dimensions of the smaller square are 2 by 2 meters, dimensions of the larger square are 4 by 4 meters.
C)Dimensions of the smaller square are 8 by 8 meters, dimensions of the larger square are 32 by 32 meters.
D)Dimensions of the smaller square are 3 by 3 meters, dimensions of the larger square are 12 by 12 meters.
E)Dimensions of the smaller square are 2 by 2 meters, dimensions of the larger square are 8 by 8 meters.

Question 46

Use the difference of squares pattern to factor the polynomial. $x ^ { 2 } - 16$

A)( x - 4)( x + 4)
B)( x + 4)( x + 16)
C)( x - 4)( x - 16)
D)( x - 16)( x + 16)
E)none of these

Question 47

Factor the polynomial completely. $$16 - 25 y ^ { 2 }$$

A)(4 + y )(4 + 5 y )
B)(4 - 5 y )(4 + 5 y )
C)(16 - 5 y )(16 + 5 y )
D)(4 - 25 y )(4 + 25 y )
E)none of these

Question 48

Factor the expression. $( a - n ) c + ( a - n ) d$

A) $( d - n ) ( c + a )$
B) $( a - d ) ( c + n )$
C) $c ( a - d ) + d$
D) $( a - n ) ( c + d )$
E) $( n - a ) ( c + d )$

Question 49

Factor the expression. Factor out any greatest common factors first. $4 x ^ { 3 } + 32$

A) $4 ( x - 2 ) \left( x ^ { 2 } + 8 x + 4 \right)$
B) $4 ( x + 4 ) \left( x ^ { 2 } + 4 x + 4 \right)$
C) $2 ( x - 2 ) \left( x ^ { 2 } + 2 x + 4 \right)$
D) $4 ( x + 2 ) \left( x ^ { 2 } - 2 x + 4 \right)$
E) $2 ( x + 4 ) \left( x ^ { 2 } + 4 x - 16 \right)$

Question 50

Factor the trinomial square and use the square root method to solve the equation. $x ^ { 2 } - 5 x + 9 = 9$

A) $0$
B) $\pm 5$
C) $0 , - 5$
D) $0,5$
E) $5$

Question 51

Use the difference of squares pattern to factor the polynomial. $x ^ { 2 } - 9 y ^ { 2 }$

A)( x - 9 y )( x + 9 y )
B)( x + 3 y )( x + 9 y )
C)( x - 3 y )( x + 3 y )
D)( x - 3 y )( x - 9 y )
E)none of these

Question 52

Factor the polynomial. $x ^ { 3 } + 8$

A) $( x + 2 ) \left( x ^ { 2 } - 2 x + 4 \right)$
B) $( x - 2 ) \left( x ^ { 2 } - 2 x + 4 \right)$
C) $( x + 2 ) \left( x ^ { 2 } - 2 x - 4 \right)$
D) $( x + 2 ) ^ { 3 }$
E) $( x - 2 ) ^ { 3 }$

Question 53

Factor by grouping. $$a x ^ { 2 } - x ^ { 2 } + 7 a - 7$$

A) $x ^ { 2 } + 7 ( a - 1 )$
B) $a x ^ { 2 } + 7 a - \left( x ^ { 2 } + 7 \right)$
C) $\left( x ^ { 2 } + 7 \right) ( a - 1 )$
D) $\left( x ^ { 2 } - 7 \right) a + x ^ { 2 } + 7$
E) $\left( x ^ { 2 } + 7 \right) a - x ^ { 2 } - 7$

Question 54

Factor the expression. $$33 a ^ { 2 } b ^ { 2 } ( 7 x - 2 y ) - 6 a b ( 7 x - 2 y )$$

A) $3 a b ( 7 x - 2 y ) ( 11 a b - 2 )$
B) $3 a b ( 7 x - 2 y ) ( 11 a b - 2 )$ .
C) $3 a b ( 7 x + 2 y ) ( 11 a b - 2 )$
D) $3 a b ( 7 x - 2 y ) ( 11 a b - 2 a b )$
E) $3 a b ( 7 x - 2 y ) ( 11 a b + 2 a b )$ .

Question 55

Use the rational root theorem and the factor theorem to help solve the equation. x ³ - x ² - 65 x + 225 = 0

A){-9, 5}
B){-5, 9}
C){-8 , 3}
D){-9, 3}
E){-8, 5}

Question 56

Use the sum-of-two-cubes or the difference-of-two-cubes pattern to factor the following. 1 - 27 a ³

A)( 1 - 3 a )( 1 - 6 a + 9 a ² )
B)( 1 - 3 a )( 1 - 3 a + 9 a ² )
C)( 1 - 3 a )( 1 + 3 a + 9 a ² )
D)( 1 + 3 a )( 1 + 3 a + 9 a ² )
E)( 1 - 3 a )( 1 + 6 a + 9 a ² )

Question 57

Factor completely. $$5 x ( 9 a + b ) - 17 y ( 9 a + b )$$

A) $( 5 x - 17 y ) ( 9 a + b )$
B) $45 a x - 153 a y - 5 b x + 34 b y$
C) $5 x - 17 y ( 9 a + b )$
D) $( 5 x - 17 y ) 9 a + b$
E) $45 a x - 153 a y + 5 b x - 17 b y$

Question 58

Find two integers whose product is 77 such that one of the integers is three less than twice the other integer.

A)8, 12
B)8, 10
C)6, 12
D)6, 10
E)7, 11

Question 59

Use the factoring method to solve the equation. $$6 x ^ { 2 } + 11 x + 4 = 0$$

A) $- \frac { 4 } { 3 }$ , $- \frac { 1 } { 2 }$
B) $\frac { 1 } { 2 }$ , $\frac { 4 } { 3 }$
C) $- \frac { 1 } { 2 }$ , $\frac { 4 } { 3 }$
D) $- \frac { 4 } { 3 }$ , $\frac { 4 } { 3 }$
E) $- \frac { 4 } { 3 }$ , $\frac { 1 } { 2 }$

Question 60

Factor the expression. $$( x - 12 ) ^ { 2 } + ( x - 12 )$$

A) $( x - 12 ) ( x + 11 )$
B) $( x - 14 ) ( x - 11 )$
C) $( x - 12 ) ( x - 13 )$
D) $( x - 12 ) ( x + 13 )$
E) $( x - 12 ) ( x - 11 )$

Question 61

Factor completely the polynomial. Indicate any that are not factorable using integers. x ² - 10 x + 21

A)( x + 3)( x + 7)
B)( x + 3)( x - 7)
C)( x - 3)( x - 7)
D)( x - 3)( x + 7)
E)not factorable

Question 62

Factor completely the polynomial. Indicate any that are not factorable using integers. a ² - 4 a + 21

A)( a - 3)( a + 7)
B)( a + 3)( a - 7)
C)( a - 3)( a - 7)
D)( a + 3)( a + 7)
E)not factorable

Question 63

The length of an altitude of a triangle is $\frac { 1 } { 2 }$ the length of the side to which it is drawn. If the area of the triangle is 75 square centimeters, find the length of that altitude.

A)5 centimeters
B)4 centimeters
C)10 centimeters
D)3 centimeters
E)8 centimeters

Question 64

Factor completely the polynomial. Indicate any that are not factorable using integers. x ² + 10 xy + 24 y ²

A)( x + 4 y )( x - 6 y )
B)( x + 4 y )( x + 6 y )
C)( x - 4 y )( x + 6 y )
D)( x - 4 y )( x - 6 y )
E)not factorable

Question 65

Suppose that the length of a rectangle is 9 and one-third times as long as its width. The area of the rectangle is 1,344 square centimeters. Find the length and width of the rectangle.

A)The width of the rectangle is 12 and the length of the rectangle is 112.
B)The width of the rectangle is 17 and the length of the rectangle is 122.
C)The width of the rectangle is 11 and the length of the rectangle is 28.
D)The width of the rectangle is 14 and the length of the rectangle is 117.
E)The width of the rectangle is 10 and the length of the rectangle is 112.

Question 66

Factor the expression. 8 g - rn - 8 n + rg

A)(8 - n )( g + r )
B)(8 + n )( g - r )
C)( g - n )(8 + r )
D)( g - n )(8 - r )
E)( g + n )(8 - r )

Question 67

Factor the polynomial. $2 ( x + y ) ^ { 2 } + ( x + y ) - 3$

A) $( x + y + 3 ) ( 2 x + 2 y - 1 )$
B) $( x + y + 1 ) ( 2 x + 2 y - 1 )$
C) $( x + y + 3 ) ( x + y - 1 )$
D) $( 2 x + 2 y + 1 ) ( x + y - 1 )$
E) $( 2 x + 2 y + 3 ) ( x + y - 1 )$

Question 68

Solve the equation. $x ^ { 3 } - 7 x ^ { 2 } + 12 x = 0$

A)1, 4 , 3
B)0, 4, 3
C)4 , 3
D)-4, -3
E)0, -4 , -3

Question 69

Factor the expression. $$2 x ^ { 3 } z - 4 x ^ { 2 } z + 28 x z - 56 z$$

A) $2 z ( x - 2 ) \left( x ^ { 2 } + 14 \right)$
B) $2 z ( x + 2 ) \left( x ^ { 2 } - 14 \right)$
C) $2 z ( x + 2 ) \left( x ^ { 2 } + 28 \right)$
D) $2 z ( x + 2 ) \left( x ^ { 2 } + 14 \right)$
E) $2 z ( x - 2 ) \left( x ^ { 2 } - 14 \right)$

Question 70

Factor the expression. $x ^ { 2 } + 8 x + 1$

A) $( 3 x + 5 ) ( x + 5 )$
B) $( 2 x + 5 ) ( x + 5 )$
C) $( 2 x + 3 ) ( x - 5 )$
D) $( 2 x - 5 ) ( x + 4 )$
E)prime

Question 71

Find two integers whose product is 405 such that one of the integers is three less than twice the other integer.

A)16, 26
B)14, 26
C)15, 27
D)16, 28
E)14, 28

Question 72

The combined area of two squares is 104 square meters. The sides of the larger square are 5 times as long as the sides of the smaller square. Find the dimensions of each of the squares.

A)Dimensions of the smaller square are 1 by 1 meters, dimensions of the larger square are 2 by 2 meters.
B)Dimensions of the smaller square are 2 by 2 meters, dimensions of the larger square are 10 by 10 meters.
C)Dimensions of the smaller square are 3 by 3 meters, dimensions of the larger square are 15 by 15 meters.
D)Dimensions of the smaller square are 7 by 7 meters, dimensions of the larger square are 35 by 35 meters.
E)Dimensions of the smaller square are 1 by 1 meters, dimensions of the larger square are 5 by 5 meters.

Question 73

Factor the expression. $$- 20 a b c - 20 a c ^ { 2 } + 4 b c + 4 c ^ { 2 }$$

A) $- 4 c ( b - c ) ( 5 a + 1 )$
B) $- 4 c ( b - 1 ) ( 5 a + c )$
C) $- 4 c ( b + c ) ( 5 a - 1 )$
D) $4 c ( b - 1 ) ( 5 a + c )$
E) $- 4 c ( b + 1 ) ( 5 a - c )$

Question 74

Factor the trinomial square and use the square root method to solve the equation. $3 x ^ { 2 } + 7 x + 1 = 2$

A) $\frac { ( - 10 + \sqrt { 61 } ) } { 7 }$ , $\frac { ( - 10 - \sqrt { 61 } ) } { 7 }$
B) $\frac { ( - 6 + \sqrt { 61 } ) } { 7 }$ , $\frac { ( - 6 - \sqrt { 61 } ) } { 7 }$
C) $\frac { ( - 7 + \sqrt { 61 } ) } { 6 }$ , $\frac { ( - 7 - \sqrt { 61 } ) } { 6 }$
D) $\frac { ( - 8 \sqrt { 61 } ) } { 7 }$ , $\frac { ( - 8 - \sqrt { 61 } ) } { 7 }$

Question 75

Use the rational root theorem and the factor theorem to help solve the equation. Be sure that the number of solutions for the equation agrees with property of number solutions of a polynomial equation, taking into account multiplicity of solutions. $2 x ^ { 4 } + x ^ { 3 } - 16 x ^ { 2 } - 3 x + 30 = 0$

A) $\left\{ - \frac { 5 } { 2 } , 2 , \pm \sqrt { 3 } \right\}$
B) $\left\{ - \frac { 3 } { 2 } , - 2 , \pm \sqrt { 3 } \right\}$
C) $\left\{ - \frac { 5 } { 2 } , - 1 \pm \sqrt { 3 } \right\}$
D) $\left\{ - \frac { 9 } { 2 } , 1 \pm \sqrt { 3 } \right\}$
E) $\left\{ - \frac { 5 } { 2 } , - 2 , \pm \sqrt { 3 } \right\}$

Question 76

Factor the expression. $a ^ { 2 } - 4 a + 4$

A) $( a + 2 ) ( a + 2 )$
B) $( a - 2 ) ( a + 2 )$
C) $( a + 4 ) ( a + 1 )$
D) $( a - 2 ) ( a - 2 )$
E)prime

Question 77

Factor completely the polynomial. Indicate any that are not factorable using integers. 24 x ² + 58 x + 35

A)(4 x - 5)(6 x - 7)
B)(4 x + 5)(6 x - 7)
C)(4 x - 5)(6 x + 7)
D)(4 x + 5)(6 x + 7)
E)not factorable

Question 78

Completely factor the expression. $$3 a ^ { 2 } x ^ { 2 } + 12 a ^ { 2 } x + 12 a ^ { 2 } - 6 b ^ { 2 } x ^ { 2 } - 24 b ^ { 2 } x - 24 b ^ { 2 }$$

A) $3 ( x - 2 ) ^ { 2 } \left( a ^ { 2 } - 2 b ^ { 2 } \right)$
B) $3 ( x + 2 ) ^ { 2 } \left( a ^ { 2 } + 2 b ^ { 2 } \right)$
C) $3 ( x - 2 ) ^ { 2 } \left( a ^ { 2 } + 2 b ^ { 2 } \right)$
D) $3 ( x + 2 ) ^ { 2 } \left( a ^ { 2 } - 2 b ^ { 2 } \right)$
E)prime

Question 79

Factor the following perfect square trinomial. $c ^ { 2 } + 14 c + 49$

A) $( c - 7 ) ^ { 2 }$
B) $( c + 6 ) ^ { 2 }$
C) $( c + 14 ) ^ { 2 }$
D) $( c + 7 ) ^ { 2 }$
E)none of these

Question 80

Use the rational root theorem and the factor theorem to help solve the equation. x ³ - 3 x ² + x - 3 = 0

A) $\{ 3 , \pm i \}$
B) $\{ 3,3 , \pm i \}$
C) $\{ 2 , \pm i \}$
D) $\{ 2,3 , \pm i \}$
E) $\{ 4 , \pm 2 i \}$