Question 1

Factor.
-$16 x ^ { 2 } - 40 x + 25$

Accepted Answer

A)  $( 4 x - 5 ) ( 4 x + 5 )$ 
B)  $( 4 x + 5 ) ^ { 2 }$ 
C)  $( 16 x + 1 ) ( x + 25 )$ 
D)  $( 4 x - 5 ) ^ { 2 }$ 
A)  $( 4 x - 5 ) ( 4 x + 5 )$ 
B)  $( 4 x + 5 ) ^ { 2 }$ 
C)  $( 16 x + 1 ) ( x + 25 )$ 
D)  $( 4 x - 5 ) ^ { 2 }$

Question 2

Factor the polynomial completely.
-$12 x ^ { 2 } - 42 x - 24$

Accepted Answer

A)  $6 ( 2 x + 1 ) ( x - 4 )$ 
B)  prime polynomial 
C)  $6 ( 2 x - 1 ) ( x + 4 )$ 
D)  $( 12 x - 6 ) ( x + 4 )$ 
A)  $6 ( 2 x + 1 ) ( x - 4 )$ 
B)  prime polynomial 
C)  $6 ( 2 x - 1 ) ( x + 4 )$ 
D)  $( 12 x - 6 ) ( x + 4 )$

Question 3

Factor the polynomial completely.
-$15 x ^ { 2 } + 14 x y - 8 y ^ { 2 }$

Accepted Answer

A)  $( 15 x + 4 y ) ( x - 2 y )$ 
B)  $( 3 x + 4 y ) ( 5 x - 2 y )$ 
C)  $( 3 x - 4 y ) ( 5 x + 2 y )$ 
D)  prime polynomial 
A)  $( 15 x + 4 y ) ( x - 2 y )$ 
B)  $( 3 x + 4 y ) ( 5 x - 2 y )$ 
C)  $( 3 x - 4 y ) ( 5 x + 2 y )$ 
D)  prime polynomial

Question 4

Factor the polynomial by grouping.
-$2 y - 16 + x y - 8 x$

Accepted Answer

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

Question 5

Use synthetic division to divide.
-$$\frac { x ^ { 2 } + 5 x - 84 } { x - 7 }$$

Accepted Answer

A)  $x + 12 - \frac { 168 } { x - 7 }$ 
B)  $x - 12$ 
C)  $x - 12 - \frac { 168 } { x - 7 }$ 
D)  $x + 12$ 
A)  $x + 12 - \frac { 168 } { x - 7 }$ 
B)  $x - 12$ 
C)  $x - 12 - \frac { 168 } { x - 7 }$ 
D)  $x + 12$

Question 6

Factor the trinomial.
-$15 x ^ { 2 } + 29 x + 12$

Accepted Answer

A)  $( 15 x + 4 ) ( x + 3 )$ 
B)  $( 3 x + 4 ) ( 5 x + 3 )$ 
C)  $( 3 x - 4 ) ( 5 x - 3 )$ 
D)  prime polynomial 
A)  $( 15 x + 4 ) ( x + 3 )$ 
B)  $( 3 x + 4 ) ( 5 x + 3 )$ 
C)  $( 3 x - 4 ) ( 5 x - 3 )$ 
D)  prime polynomial

Question 7

Factor.
-$$8 - x ^ { 3 }$$

Accepted Answer

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

Question 8

Multiply.
-$12 x y ( 3 x - 10 y )$

Accepted Answer

A)  $36 x ^ { 2 } y - 120 x y ^ { 2 }$ 
B)  $15 x ^ { 2 } - 22 y ^ { 2 }$ 
C)  $15 x ^ { 2 } y - 22 x y ^ { 2 }$ 
D)  $36 x ^ { 2 } - 120 y ^ { 2 }$ 
A)  $36 x ^ { 2 } y - 120 x y ^ { 2 }$ 
B)  $15 x ^ { 2 } - 22 y ^ { 2 }$ 
C)  $15 x ^ { 2 } y - 22 x y ^ { 2 }$ 
D)  $36 x ^ { 2 } - 120 y ^ { 2 }$

Question 9

Factor the polynomial.
-$$15 a ^ { 3 } - 9 a ^ { 2 } b - 20 a b ^ { 2 } + 12 b ^ { 3 }$$

Accepted Answer

A)  $\left( 3 a ^ { 2 } - 4 b ^ { 2 } \right) ( 5 a - 3 b )$ 
B)  $\left( 3 a ^ { 2 } - 4 b \right) ( 5 a - 3 b )$ 
C)  $\left( 15 a ^ { 2 } - 4 b ^ { 2 } \right) ( a - 3 b )$ 
D)  $\left( 3 a ^ { 2 } + 4 b ^ { 2 } \right) ( 5 a + 3 b )$ 
A)  $\left( 3 a ^ { 2 } - 4 b ^ { 2 } \right) ( 5 a - 3 b )$ 
B)  $\left( 3 a ^ { 2 } - 4 b \right) ( 5 a - 3 b )$ 
C)  $\left( 15 a ^ { 2 } - 4 b ^ { 2 } \right) ( a - 3 b )$ 
D)  $\left( 3 a ^ { 2 } + 4 b ^ { 2 } \right) ( 5 a + 3 b )$

Question 10

Find all positive and negative integers b such that the trinomial is factorable.
-$$11 x ^ { 2 } + b x + 1$$

Accepted Answer

A)  12 
B)  $$\pm 12$$ 
C)  10 
D)  $$\pm 10$$ 
A)  12 
B)  $$\pm 12$$ 
C)  10 
D)  $$\pm 10$$

Factor. - $16 x ^ { 2 } - 40 x + 25$

Factor the polynomial completely. - $12 x ^ { 2 } - 42 x - 24$

Factor the polynomial completely. - $15 x ^ { 2 } + 14 x y - 8 y ^ { 2 }$

Factor the polynomial by grouping. - $2 y - 16 + x y - 8 x$

Use synthetic division to divide. - $\frac { x ^ { 2 } + 5 x - 84 } { x - 7 }$

Factor the trinomial. - $15 x ^ { 2 } + 29 x + 12$

Factor. - $8 - x ^ { 3 }$

Multiply. - $12 x y ( 3 x - 10 y )$

Factor the polynomial. - $15 a ^ { 3 } - 9 a ^ { 2 } b - 20 a b ^ { 2 } + 12 b ^ { 3 }$

Find all positive and negative integers b such that the trinomial is factorable. - $11 x ^ { 2 } + b x + 1$

Real Numbers and Algebraic Expressions

Equations, Inequalities, and Problem Solving

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Systems of Equations and Inequalities

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Exponential and Logarithmic Functions

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Exam 5: Polynomials and Polynomial Functions

Factor. - 16x2−40x+2516 x ^ { 2 } - 40 x + 2516x2−40x+25

Factor the polynomial completely. - 12x2−42x−2412 x ^ { 2 } - 42 x - 2412x2−42x−24

Factor the polynomial completely. - 15x2+14xy−8y215 x ^ { 2 } + 14 x y - 8 y ^ { 2 }15x2+14xy−8y2

Factor the polynomial by grouping. - 2y−16+xy−8x2 y - 16 + x y - 8 x2y−16+xy−8x

Use synthetic division to divide. - x2+5x−84x−7\frac { x ^ { 2 } + 5 x - 84 } { x - 7 }x−7x2+5x−84​

Factor the trinomial. - 15x2+29x+1215 x ^ { 2 } + 29 x + 1215x2+29x+12

Factor. - 8−x38 - x ^ { 3 }8−x3

Multiply. - 12xy(3x−10y)12 x y ( 3 x - 10 y )12xy(3x−10y)

Factor the polynomial. - 15a3−9a2b−20ab2+12b315 a ^ { 3 } - 9 a ^ { 2 } b - 20 a b ^ { 2 } + 12 b ^ { 3 }15a3−9a2b−20ab2+12b3

Find all positive and negative integers b such that the trinomial is factorable. - 11x2+bx+111 x ^ { 2 } + b x + 111x2+bx+1