Question 1

Factor completely.
-$$\left( x ^ { 2 } - 4 \right) ^ { 2 } - 4 \left( x ^ { 2 } - 4 \right) - 96$$

Accepted Answer

The given expression can be rewritten as a quadratic in terms of $y = x^2 - 4$, resulting in $y^2 - 4y - 96$. Factoring this quadratic gives $(y - 12)(y + 8)$. Substituting back $x^2 - 4$ for $y$, we get $(x^2 - 4 - 12)(x^2 - 4 + 8)$, which simplifies to $(x^2 - 16)(x^2 + 4)$, or $(x + 4)(x - 4)(x^2 + 4)$.

Question 2

Factor completely.
-$$9 x ^ { 4 } + 21 x ^ { 3 } - 9 x ^ { 2 } - 21 x$$

Accepted Answer

First, factor out the greatest common factor, which is $3x$, giving $3x(3x^3 + 7x^2 - 3x - 7)$. Then, use grouping: group $3x^3 + 7x^2$ and $-3x - 7$, factoring each group to get $3x((3x^2)(x + \frac{7}{3}) - 1(x + \frac{7}{3}))$, which simplifies to $3x(3x^2 - 1)(x + \frac{7}{3})$. Factoring $3x^2 - 1$ as a difference of squares gives $3x(x + 1)(x - 1)(3x + 7)$.

Question 3

Factor completely.
-$$( c - 9 ) ^ { 2 } - ( 4 c - 2 ) ^ { 2 }$$

Accepted Answer

The correct answer is B because:$$( c - 9 ) ^ { 2 } - ( 4 c - 2 ) ^ { 2 } = ( c - 9 + 4 c - 2 ) ( c - 9 - 4 c + 2 ) = ( 5 c - 11 ) ( - 3 c - 7 )$$

Question 4

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-The ratio of a polynomial and its opposite equals .

Accepted Answer

The answer of Write the word or phrase that best...

Question 5

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-The expression $$\frac { 5 ( x + 2 ) } { ( x + 2 ) ( x - 1 ) }$$ equals $\frac { 5 } { x - 1 }$ provided that $x \neq$ـــــــــــــــــ and $x \neq$ـــــــــــــــــ

Accepted Answer

The answer of Write the word or phrase that best...

Question 6

Factor completely.
-$$( a + 7 ) ^ { 2 } - y ^ { 2 }$$

Accepted Answer

This expression is a difference of squares, which factors as $(a+7)^2 - y^2 = (a+7+y)(a+7-y)$.

Question 7

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-The restricted values of the variable for a rational expression are those that make the denominator
equal to .

Accepted Answer

The answer of Write the word or phrase that best...

Question 8

Factor completely.
-$$x ( 2 x + 1 ) ^ { - 2 / 3 } + ( 2 x + 1 ) ^ { 1 / 3 }$$

Accepted Answer

The expression can be factored by taking out the common factor $(2x + 1)^{-2/3}$, resulting in $(2x + 1)^{-2/3}(x + (2x + 1))$, which simplifies to $\frac{3x + 1}{(2x + 1)^{2/3}}$.

Question 9

Factor completely.
-$m ^ { 6 } + 124 m ^ { 3 } - 125$

Accepted Answer

The answer of Factor completely.
-\(m ^ { 6 } +...

Question 10

Factor completely.
-$$x ^ { 2 } + 3 x y - 4 y ^ { 2 } - 5 y + 5 x$$

Accepted Answer

The answer of Factor completely.
-\[x ^ { 2 } +...

Question 11

Factor completely.
-$$8 x ^ { - 7 } + 4 x ^ { - 6 } + x ^ { - 5 }$$

Accepted Answer

The answer of Factor completely.
-\[8 x ^ { - 7...

Question 12

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-A expression is a ratio of two polynomials.

Accepted Answer

The answer of Write the word or phrase that best...

Question 13

Factor completely.
-$3 c ^ { 9 / 5 } - 3 c ^ { 4 / 5 }$

Accepted Answer

The correct factorization is found by taking out the common factor of $3c^{4/5}$ from both terms, leaving $3c^{4/5}(c^{5/5}-1)$, which simplifies to $3c^{4/5}(c-1)$.

Question 14

Factor completely.
-$27 u ^ { 6 } - 8 v ^ { 6 }$

Accepted Answer

The answer of Factor completely.
-\(27 u ^ { 6 }...

Question 15

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-A fraction is an expression that contains one or more fractions in the numerator or
denominator.

Accepted Answer

The answer of Write the word or phrase that best...

Question 16

Factor completely.
-$12 x ^ { 5 } - 27 x ^ { 3 }$

Accepted Answer

The answer of Factor completely.
-\(12 x ^ { 5 }...

Question 17

Factor the sum or difference of cubes.
-$125 r ^ { 3 } + 8$

Accepted Answer

The sum of cubes can be factored using the formula $a^3 + b^3 = (a + b)(a^2 - ab + b^2)$. Here, $125r^3 = (5r)^3$ and $8 = 2^3$, so applying the formula gives $(5r + 2)(25r^2 - 10r + 4)$.

Question 18

Factor completely.
-$$9 x ^ { 2 } - 25 y ^ { 2 }$$

Accepted Answer

This expression is a difference of squares, factored as $(a + b)(a - b)$ where $a = 3x$ and $b = 5y$.

Question 19

Factor completely.
-$$5 x ^ { 7 / 2 } - \frac { 5 } { 2 } x ^ { - 7 / 2 }$$

Accepted Answer

The answer of Factor completely.
-\[5 x ^ { 7 /...

Question 20

Factor completely.
-$12 x ^ { - 6 } + 7 x ^ { - 5 } + x ^ { - 4 }$

Accepted Answer

The answer of Factor completely.
-\(12 x ^ { - 6...

Quiz 9: Review of Prerequisites

Factor completely. - $\left( x ^ { 2 } - 4 \right) ^ { 2 } - 4 \left( x ^ { 2 } - 4 \right) - 96$

Factor completely. - $9 x ^ { 4 } + 21 x ^ { 3 } - 9 x ^ { 2 } - 21 x$

Factor completely. - $( c - 9 ) ^ { 2 } - ( 4 c - 2 ) ^ { 2 }$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The ratio of a polynomial and its opposite equals .

Factor completely. - $( a + 7 ) ^ { 2 } - y ^ { 2 }$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The restricted values of the variable for a rational expression are those that make the denominator equal to .

Factor completely. - $x ( 2 x + 1 ) ^ { - 2 / 3 } + ( 2 x + 1 ) ^ { 1 / 3 }$

Factor completely. - $m ^ { 6 } + 124 m ^ { 3 } - 125$

Factor completely. - $x ^ { 2 } + 3 x y - 4 y ^ { 2 } - 5 y + 5 x$

Factor completely. - $8 x ^ { - 7 } + 4 x ^ { - 6 } + x ^ { - 5 }$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -A expression is a ratio of two polynomials.

Factor completely. - $3 c ^ { 9 / 5 } - 3 c ^ { 4 / 5 }$

Factor completely. - $27 u ^ { 6 } - 8 v ^ { 6 }$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -A fraction is an expression that contains one or more fractions in the numerator or denominator.

Factor completely. - $12 x ^ { 5 } - 27 x ^ { 3 }$

Factor the sum or difference of cubes. - $125 r ^ { 3 } + 8$

Factor completely. - $9 x ^ { 2 } - 25 y ^ { 2 }$

Factor completely. - $5 x ^ { 7 / 2 } - \frac { 5 } { 2 } x ^ { - 7 / 2 }$

Factor completely. - $12 x ^ { - 6 } + 7 x ^ { - 5 } + x ^ { - 4 }$

Quiz 9: Review of Prerequisites

Factor completely. - (x2−4) 2−4(x2−4) −96\left( x ^ { 2 } - 4 \right) ^ { 2 } - 4 \left( x ^ { 2 } - 4 \right) - 96(x2−4) 2−4(x2−4) −96

Factor completely. - 9x4+21x3−9x2−21x9 x ^ { 4 } + 21 x ^ { 3 } - 9 x ^ { 2 } - 21 x9x4+21x3−9x2−21x

Factor completely. - (c−9) 2−(4c−2) 2( c - 9 ) ^ { 2 } - ( 4 c - 2 ) ^ { 2 }(c−9) 2−(4c−2) 2

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The ratio of a polynomial and its opposite equals .

Factor completely. - (a+7) 2−y2( a + 7 ) ^ { 2 } - y ^ { 2 }(a+7) 2−y2

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The restricted values of the variable for a rational expression are those that make the denominator equal to .

Factor completely. - x(2x+1) −2/3+(2x+1) 1/3x ( 2 x + 1 ) ^ { - 2 / 3 } + ( 2 x + 1 ) ^ { 1 / 3 }x(2x+1) −2/3+(2x+1) 1/3

Factor completely. - m6+124m3−125m ^ { 6 } + 124 m ^ { 3 } - 125m6+124m3−125

Factor completely. - x2+3xy−4y2−5y+5xx ^ { 2 } + 3 x y - 4 y ^ { 2 } - 5 y + 5 xx2+3xy−4y2−5y+5x

Factor completely. - 8x−7+4x−6+x−58 x ^ { - 7 } + 4 x ^ { - 6 } + x ^ { - 5 }8x−7+4x−6+x−5

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -A expression is a ratio of two polynomials.

Factor completely. - 3c9/5−3c4/53 c ^ { 9 / 5 } - 3 c ^ { 4 / 5 }3c9/5−3c4/5

Factor completely. - 27u6−8v627 u ^ { 6 } - 8 v ^ { 6 }27u6−8v6

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -A fraction is an expression that contains one or more fractions in the numerator or denominator.

Factor completely. - 12x5−27x312 x ^ { 5 } - 27 x ^ { 3 }12x5−27x3

Factor the sum or difference of cubes. - 125r3+8125 r ^ { 3 } + 8125r3+8

Factor completely. - 9x2−25y29 x ^ { 2 } - 25 y ^ { 2 }9x2−25y2

Factor completely. - 5x7/2−52x−7/25 x ^ { 7 / 2 } - \frac { 5 } { 2 } x ^ { - 7 / 2 }5x7/2−25​x−7/2

Factor completely. - 12x−6+7x−5+x−412 x ^ { - 6 } + 7 x ^ { - 5 } + x ^ { - 4 }12x−6+7x−5+x−4

Factor completely. - $\left( x ^ { 2 } - 4 \right) ^ { 2 } - 4 \left( x ^ { 2 } - 4 \right) - 96$

Factor completely. - $9 x ^ { 4 } + 21 x ^ { 3 } - 9 x ^ { 2 } - 21 x$

Factor completely. - $( c - 9 ) ^ { 2 } - ( 4 c - 2 ) ^ { 2 }$

Factor completely. - $( a + 7 ) ^ { 2 } - y ^ { 2 }$

Factor completely. - $x ( 2 x + 1 ) ^ { - 2 / 3 } + ( 2 x + 1 ) ^ { 1 / 3 }$

Factor completely. - $m ^ { 6 } + 124 m ^ { 3 } - 125$

Factor completely. - $x ^ { 2 } + 3 x y - 4 y ^ { 2 } - 5 y + 5 x$

Factor completely. - $8 x ^ { - 7 } + 4 x ^ { - 6 } + x ^ { - 5 }$

Factor completely. - $3 c ^ { 9 / 5 } - 3 c ^ { 4 / 5 }$

Factor completely. - $27 u ^ { 6 } - 8 v ^ { 6 }$

Factor completely. - $12 x ^ { 5 } - 27 x ^ { 3 }$

Factor the sum or difference of cubes. - $125 r ^ { 3 } + 8$

Factor completely. - $9 x ^ { 2 } - 25 y ^ { 2 }$

Factor completely. - $5 x ^ { 7 / 2 } - \frac { 5 } { 2 } x ^ { - 7 / 2 }$

Factor completely. - $12 x ^ { - 6 } + 7 x ^ { - 5 } + x ^ { - 4 }$