Deck 7: Factoring, Solving Equations and Problem Solving

Question 1

Factor the polynomial completely. $2 y ( d + 5 ) + 9 f ( d + 5 )$

A) $( 2 y + 9 f ) ( d + 5 )$
B) $( 2 y + 9 f ) ( d + 90 )$
C) $( 9 y + 2 f ) ( d + 5 )$
D) $2 y + 9 f ( d + 5 )$
E) $( 2 y + 9 f ) d + 5$

Answer 1

$( 2 y + 9 f ) ( d + 5 )$

Question 2

Factor the polynomial completely. $9 z ^ { 4 } d ^ { 9 } + 4 z ^ { 12 } d ^ { 5 }$

A) $z ^ { 4 } d ^ { 5 } ( 9 d + 4 z )$
B) $36 z ^ { 4 } d ^ { 5 } \left( 9 d ^ { 4 } + 4 z ^ { 8 } \right)$
C) $z ^ { 4 } d ^ { 5 } \left( 9 d ^ { 4 } - 4 z ^ { 12 } \right)$
D) $z ^ { 4 } d ^ { 5 } \left( 9 d ^ { 4 } + 4 z ^ { 8 } \right)$

Answer 2

$z ^ { 4 } d ^ { 5 } \left( 9 d ^ { 4 } + 4 z ^ { 8 } \right)$

Question 3

Factor the polynomial completely. $7 z ^ { 6 } + 7 z ^ { 7 } + 7 z ^ { 4 }$

A) $7 z ^ { 4 } \left( z ^ { 2 } + z ^ { 3 } + z \right)$
B) $7 z ^ { 4 } \left( z ^ { 2 } + z ^ { 3 } + 7 \right)$
C) $7 z ^ { 4 } \left( z ^ { 2 } + z ^ { 3 } + 1 \right)$

Answer 3

$7 z ^ { 4 } \left( z ^ { 2 } + z ^ { 3 } + 1 \right)$

Question 4

Factor the polynomial completely. $20 y ^ { 3 } d ^ { 2 } + 32 y d ^ { 4 } + 68 y d ^ { 2 }$

A) $4 y d ^ { 2 } \left( 5 y d ^ { 2 } + 8 d ^ { 4 } + 17 \right)$
B) $4 y d ^ { 2 } \left( 5 y d ^ { 2 } + 8 d ^ { 2 } + 17 y \right)$
C) $4 y d ^ { 2 } \left( 5 y ^ { 2 } + 8 d ^ { 2 } + 17 \right)$
D) $4 y d ^ { 2 } \left( 5 d y ^ { 2 } + 8 d ^ { 2 } + 17 \right)$
E) $4 y d ^ { 2 } \left( 5 y ^ { 2 } + 8 d ^ { 2 } + 34 \right)$

Question 5

When solving a word problem involving distances, a solution to the equation might be discarded.

Question 6

Factor the polynomial completely. $45 y + 65 d$

A) $65 ( y + d )$
B) $5 ( 65 y + 45 d )$
C) $45 ( y + d )$
D) $5 ( 9 y + 13 d )$
E) $115 ( 9 y - 13 d )$

Question 7

Factor the polynomial completely. $5 z ^ { 5 } b ^ { 8 } + 11 z ^ { 11 } b ^ { 3 }$

A) $55 z ^ { 5 } b ^ { 3 } \left( 5 b ^ { 5 } + 11 z ^ { 6 } \right)$
B) $z ^ { 5 } b ^ { 3 } \left( 5 b ^ { 5 } - 11 z ^ { 11 } \right)$
C) $z ^ { 5 } b ^ { 3 } \left( 5 b ^ { 5 } + 11 z ^ { 6 } \right)$
D) $z ^ { 5 } b ^ { 3 } \left( 5 b ^ { 5 } - 11 z ^ { 6 } \right)$
E) $z ^ { 5 } b ^ { 3 } ( 5 b + 11 z )$

Question 8

Find the greatest common factor of the given expression. $42 x \text { and } 66 x b$

A) $6 x$
B) $6 \times b$
C) $6$
D) $11 b$
E) $7 x$

Question 9

Factor the polynomial completely. $3 x ^ { 7 } + 3 x ^ { 8 } + 3 x ^ { 5 }$

A) $3 x ^ { 5 } \left( x ^ { 2 } + x ^ { 3 } + 3 \right)$
B) $3 x ^ { 5 } \left( x ^ { 2 } + x ^ { 3 } + x \right)$
C) $3 x ^ { 5 } \left( x ^ { 2 } + x ^ { 4 } + x \right)$
D) $3 x ^ { 5 } \left( x ^ { 2 } + x ^ { 3 } \right)$
E) $3 x ^ { 5 } \left( x ^ { 2 } + x ^ { 3 } + 1 \right)$

Question 10

If the product of a and b is zero, then a is zero or b is zero, but not both.

Question 11

Find the greatest common factor of the given expression. $15 z ^ { 4 } c ^ { 6 } , 10 z ^ { 3 } c ^ { 7 } \text { and } 55 z ^ { 6 } c ^ { 2 }$

A) $2 c ^ { 5 }$
B) $5 z c ^ { 4 }$
C) $3 z ^ { 8 } c ^ { 2 }$
D) $5 z ^ { 3 } c ^ { 2 }$

Question 12

Greatest common factors are always monomials.

Question 13

Factor the polynomial completely. $4 y ( d + 2 ) + 3 e ( d + 2 )$

A) $( 4 y + 3 e ) ( d + 24 )$
B) $4 y + 3 e ( d + 2 )$
C) $( 4 y + 3 e ) ( d + 2 )$

Question 14

The greatest common factor of two or more whole numbers can be found by using the prime factored form of the numbers.

Question 15

Find the greatest common factor of the given expressions. $45 z d , 40 z d ^ { 5 } \text { and } 65 z ^ { 2 } d$

A) $9 \mathrm { zd }$
B) $5 z d$
C) $8 d z$
D) $5 z d ^ { 2 }$

Question 16

Find the greatest common factor of the given expressions. $18 y d , 48 y d ^ { 6 } \text { and } 66 y ^ { 2 } d$

A) $6 y d$
B) $48 d y$
C) $6 y$
D) $8 d y$
E) $3 y d$

Question 17

Find the greatest common factor of the given expressions. $54 y ^ { 4 } a ^ { 9 } , 48 y ^ { 3 } a ^ { 11 } \text { and } 78 y ^ { 6 } a ^ { 5 }$

A) $8 a ^ { 9 }$
B) $6 y ^ { 3 } a ^ { 5 }$
C) $9 y ^ { 8 } a ^ { 5 }$
D) $8 a ^ { 8 }$
E) $6 y a ^ { 10 }$

Question 18

Find the greatest common factor of the given expression. $28 y \text { and } 32 y a$

A) $4 y$
B) $8 a$
C) $7 y$
D) $4 y a$

Question 19

Factor the polynomial completely. $54 z + 66 c$

A) $6 ( 66 z + 54 c )$
B) $6 ( 9 z + 11 c )$
C) $126 ( 9 z - 11 c )$

Question 20

Factor the polynomial completely. $10 p ^ { 5 } c ^ { 4 } + 16 p c ^ { 8 } + 26 p c ^ { 4 }$

A) $2 p c ^ { 4 } \left( 5 p c ^ { 4 } + 8 c ^ { 8 } + 13 \right)$
B) $2 p c ^ { 4 } \left( 5 p ^ { 4 } + 8 c ^ { 4 } + 13 \right)$
C) $2 p c ^ { 4 } \left( 5 c p ^ { 4 } + 8 c ^ { 4 } + 13 \right)$
D) $2 p c ^ { 4 } \left( 5 p c ^ { 4 } + 8 c ^ { 4 } + 13 p \right)$

Question 21

Solve the equation. $p ( 5 p - 20 ) - 5 ( 5 p - 20 ) = 0$

A) { 5, 4 }
B) { $-$ 5, 4 }
C) { $-$ 5, $-$ 4 }
D) { 5, $-$ 4 }

Question 22

Solve the equation. $9 x - x ^ { 2 } = 0$

A) $\{ 9 \}$
B) $\{ 9,0 \}$
C) $\{ 1,0 \}$
D) $\{ - 1,0 \}$
E) $\{ - 9,0 \}$

Question 23

Use the process of factoring by grouping to factor the polynomial. $- 8 z ^ { 2 } + z + 32 z - 4$

A) $( 8 z + 32 ) ( z - 1 )$
B) $( - 8 z + 1 ) ( z - 4 )$
C) $( - 8 z + 32 ) ( z - 4 )$
D) $( - 8 z - 1 ) ( z + 4 )$

Question 24

Solve the equation. $3 ( z - 9 ) - z ( z - 9 ) = 0$

A) { 3, $-$ 9 }
B) { $-$ 3, $-$ 9 }
C) { 3, 9 }
D) { $-$ 3, 9 }

Question 25

Solve the equation. $8 p ^ { 2 } = - 32 p$

A) $\{ 4,0 \}$
B) $\{ 1,0 \}$
C) $\{ - 1,0 \}$
D) $\{ 4 \}$
E) $\{ - 4,0 \}$

Question 26

Suppose that the area of a circle is numerically equal to 12 times the perimeter of a square and that the length of a radius of the circle is equal to the length of a side of the square. Find the length of a side of the square.

A) $\frac { \pi } { 48 }$
B) $\frac { 48 } { \pi }$
C) $48 \pi$

Question 27

Use the process of factoring by grouping to factor the polynomial. $4 z ^ { 2 } + z - 28 z - 7$

A) $( 4 z - 1 ) ( z + 7 )$
B) $( 4 z + 28 ) ( z - 7 )$
C) $( 4 z - 28 ) ( z - 1 )$
D) $( 4 z + 1 ) ( z - 7 )$

Question 28

Solve the equation. $4 y ^ { 2 } + 24 y = 0$

A) { $-$ 1, 0 }
B) { 1, 0 }
C) { 6, 0 }
D) { $-$ 6, 0 }
E) { 1 }

Question 29

Use the process of factoring by grouping to factor the polynomial. $7 x + 7 y + z x + z y$

A) $( x + y ) ( 7 + z )$
B) $( z + y ) ( 4 + x )$
C) $( z + y ) ( 7 + x )$
D) $( x + z ) ( 7 + y )$
E) $( x + z ) ( 4 + y )$

Question 30

Solve the equation. $7 p ^ { 2 } = - 28 p$

A) { $-$ 4, 0 }
B) { 4, 0 }
C) { 1, 0 }
D) { 1 }
E) { $-$ 1, 0 }

Question 31

Solve the equation. $21 ( z - 9 ) - z ( z - 9 ) = 0$

A) $\{ - 21 , - 9 \}$
B) $\{ 21,9 \}$
C) $\{ 21 , - 9 \}$
D) $\{ 21 \}$
E) $\{ - 21,9 \}$

Question 32

Solve the equation. $23 x - x ^ { 2 } = 0$

A) { $-$ 1, 0 }
B) { 23, 0 }
C) { 1, 0 }
D) { $-$ 23, 0 }

Question 33

Use the process of factoring by grouping to factor the polynomial. $y ^ { 2 } - 4 y - 2 y + 8$

A) $( y + 2 ) ( y + 4 )$
B) $( y - 2 ) ( y + 4 )$
C) $( y - 2 ) y - 4$
D) $( y - 2 ) ( y - 4 )$
E) $( y + 2 ) ( y - 8 )$

Question 34

Use the process of factoring by grouping to factor the polynomial. $2 z ^ { 2 } + z - 10 z - 5$

A) $( 2 z - 1 ) ( z + 5 )$
B) $( 2 z + 1 ) ( z - 5 )$
C) $( 2 z + 10 ) ( z - 5 )$
D) $( 2 z - 10 ) ( z - 1 )$
E) $( 2 z - 10 ) ( z + 1 )$

Question 35

Solve the equation. $z ^ { 2 } - 13 z = 0$

A) $\{ 1 \}$
B) $\{ 13,0 \}$
C) $\{ - 13,0 \}$
D) $\{ 1,0 \}$
E) $\{ 2 \}$

Question 36

Solve the equation. $p ^ { 2 } - 14 p = 0$

A) { 14, 0 }
B) { 1 }
C) { $-$ 14, 0 }

Question 37

Use the process of factoring by grouping to factor the polynomial. $p ^ { 2 } - 7 p - 3 p + 21$

A) $( p - 3 ) ( p - 7 )$
B) $( p + 3 ) ( p - 21 )$
C) $( p - 3 ) ( p + 7 )$

Question 38

Suppose that the area of a circle is numerically equal to 2 times the perimeter of a square and that the length of a radius of the circle is equal to the length of a side of the square. Find the length of a side of the square.

A) $\frac { \pi } { 8 }$
B) $8 \pi$
C) $\frac { \pi } { 16 }$
D) $\frac { 8 } { \pi }$
E) $\frac { 16 } { \pi }$

Question 39

The square of a number equals 20 times that number. Find the number.

A) 1
B) $-$ 20 or 0
C) 20 or 0
D) 1 or 20
E) $-$ 20 or 1

Question 40

Solve the equation. $x ( 24 x - 72 ) - 10 ( 24 x - 72 ) = 0$

A) $\{ - 10 , - 3 \}$
B) $\{ 10,0 \}$
C) $\{ 10 , - 3 \}$
D) $\{ - 10,3 \}$
E) $\{ 10,3 \}$

Question 41

Use the process of factoring by grouping to factor the polynomial.

Question 42

Factor the polynomial completely.

Question 43

Solve the equation. Please enter your answer as two numbers, separated by a comma.

Question 44

The area of a rectangle is 15 times the area of a square. If the rectangle is 75 inches long and the width of the rectangle is the same as the length of a side of the square, find the length of a side of the square.

A) 5 inches
B) 15 inches
C) 10 inches
D) 3 inches
E) 7 inches

Question 45

Factor the polynomial completely.

Question 46

Use the process of factoring by grouping to factor the polynomial.

Question 47

Factor the polynomial completely.

Question 48

The area of a rectangle is 2 times the area of a square. If the rectangle is 10 inches long and the width of the rectangle is the same as the length of a side of the square, find the length of a side of the square.

A) 1 inches
B) 10 inches
C) 7 inches
D) 5 inches

Question 49

Find the greatest common factor of the given expressions.

Question 50

Use the process of factoring by grouping to factor the polynomial.

Question 51

Factor the polynomial completely.

Question 52

Factor the polynomial completely.

Question 53

Factor the polynomial completely.

Question 54

Find the greatest common factor of the given expressions.

Question 55

The area of a rectangle is 6 times the area of a square. If the rectangle is 24 inches long and the width of the rectangle is the same as the length of a side of the square, find the length of a side of the square. __________ inches

Question 56

Find the greatest common factor of the given expression.

Question 57

Use the process of factoring by grouping to factor the polynomial.

Question 58

Solve the equation. Please enter your answer as two numbers, separated by a comma.

Question 59

Factor the polynomial completely.

Question 60

Factor the polynomial completely.

Question 61

Factor the polynomial completely. $4 a ^ { 4 } + 25 a ^ { 2 }$

A) $a ^ { 2 } \left( 4 a ^ { 2 } + 25 \right)$
B) $a ^ { 2 } \left( 4 a ^ { 2 } - 25 \right)$
C) $a \left( 4 a ^ { 3 } + 25 a \right)$
D) $a ^ { 2 } ( 2 a + 5 ) ( 2 a - 5 )$
E) none of these

Question 62

The sum of two squares is not factorable using integers.

Question 63

Solve the equation. Please enter your answer as two numbers, separated by a comma.

Question 64

For binomials of the form $x ^ { 2 } - a ^ { 2 } = 0$ , where $a \neq 0$ , there will be a negative answer and a positive answer.

Question 65

Factor the polynomial completely. $10 x ^ { 2 } + 60$

A) $10 ( x - 6 ) ( x + 6 )$
B) $10 \left( x ^ { 2 } + 6 \right)$
C) $10 \left( x ^ { 2 } - 6 \right)$
D) $10 ( x + 6 )$
E) none of these

Question 66

The difference-of-squares pattern may be used only once when solving a word problem.

Question 67

Factor the polynomial completely. Don t forget to look for a common monomial factor first. $x ^ { 2 } + 25 y ^ { 2 }$

A) $( x - 5 y ) ( x + 5 y )$
B) $( y - 10 x ) ( x + 5 y )$
C) $( x - 10 y ) ( x + 10 y )$
D) $( y - 5 x ) ( x + 5 y )$
E) not factorable

Question 68

The square of a number equals 20 times that number. Find the number. If there is more than one solution, separate your answers with commas.

Question 69

Suppose that the area of a circle is numerically equal to 25 times the perimeter of a square and that the length of a radius of the circle is equal to the length of a side of the square. Find the length of a side of the square. Leave in your answer. Please enter your answer as a fraction.

Question 70

Use the difference of squares pattern to factor the polynomial. $1 - 9 n ^ { 2 }$

A) (1 $-$ 3 n ) (1 + 3 n )
B) (1 $-$ 3 n ) (1 + 9 n )
C) (1 $-$ 9 n ) (1 + 3 n )
D) (1 $-$ 3 n )
E) none of these

Question 71

Factor the polynomial completely. $4 - 81 y ^ { 2 }$

A) (2 $-$ 81 y ) (2 + 81 y )
B) (2 $-$ 9 y ) (2 + 9 y )
C) (4 $-$ 9 y ) (4 + 9 y )
D) (2 + y ) (2 + 9 y )
E) none of these

Question 72

Solve the equation. $x ^ { 2 } = 9$

A) $x = 0$
B) $x = 19$
C) $x = \pm 9$
D) $x = \pm 3$
E) none of these

Question 73

Solve the equation. Write your answer in simplest form. If there is more than one solution, separate your answers with commas.

Question 74

Solve the equation. Please enter your answer as two numbers, separated by a comma.

Question 75

Use the difference of squares pattern to factor the polynomial. $x ^ { 2 } - 36 y ^ { 2 }$

A) ( x $-$ 6 y ) ( x $-$ 36 y )
B) ( x $-$ 36 y ) ( x + 36 y )
C) ( x $-$ 6 y ) ( x + 6 y )
D) ( x + 6 y ) ( x + 36 y )
E) none of these

Question 76

For the equation $w ^ { 2 } = 49$ in order to use the difference-of-squares factoring pattern, subtract $- 49$ from both sides.

Question 77

Solve the equation. Write your answer in simplest form. If there is more than one solution, separate your answers with commas.

Question 78

Factor the polynomial completely. Don t forget to look for a common monomial factor first. $2 x ^ { 2 } - 32 y ^ { 2 }$

A) $2 ( x - 4 y ) ( x + 4 y )$
B) $4 ( x - 2 y ) ( x + 2 y )$
C) $( x - 2 y ) ( x + 2 y )$
D) $( x - 4 y ) ( x + 4 y )$
E) not factorable

Question 79

Factor the polynomial completely. $64 - 25 m ^ { 2 }$

A) (64 $-$ 5 m ) (64 + 5 m )
B) (8 $-$ 25 m ) (8 + 25 m )
C) (8 $-$ 5 m ) (8 + 5 m )
D) (8 + m ) (8 + 5 m )
E) none of these

Question 80

Use the difference of squares pattern to factor the polynomial. $x ^ { 2 } - 49$

A) ( x $-$ 7) ( x + 7)
B) ( x $-$ 49) ( x + 49)
C) ( x + 7) ( x + 49)
D) ( x $-$ 7) ( x $-$ 49)
E) none of these