Question 1

Factor.
-$25 y ^ { 2 } - 49$

Accepted Answer

A)  $( 5 y + 7 ) ^ { 2 }$ 
B)  $( 5 y + 7 ) ( 5 y - 7 )$ 
C)  $( 5 y - 7 ) ^ { 2 }$ 
D)  prime polynomial 
A)  $( 5 y + 7 ) ^ { 2 }$ 
B)  $( 5 y + 7 ) ( 5 y - 7 )$ 
C)  $( 5 y - 7 ) ^ { 2 }$ 
D)  prime polynomial

Question 2

Factor out the greatest common factor.
-$32 x ^ { 5 } y + 28 x y ^ { 4 }$

Accepted Answer

A)  $4 y \left( 8 x ^ { 5 } + 7 x y ^ { 3 } \right)$ 
B)  $4 x y \left( 8 x ^ { 4 } + 7 y ^ { 3 } \right)$ 
C)  $4 x \left( 8 x ^ { 4 } y + 7 y ^ { 4 } \right)$ 
D)  $x y \left( 32 x ^ { 4 } + 28 y ^ { 3 } \right)$ 
A)  $4 y \left( 8 x ^ { 5 } + 7 x y ^ { 3 } \right)$ 
B)  $4 x y \left( 8 x ^ { 4 } + 7 y ^ { 3 } \right)$ 
C)  $4 x \left( 8 x ^ { 4 } y + 7 y ^ { 4 } \right)$ 
D)  $x y \left( 32 x ^ { 4 } + 28 y ^ { 3 } \right)$

Question 3

Solve the equation.
-$$x ( 6 x + 5 ) ( x - 1 ) = 0$$

Accepted Answer

A)  $\left\{ - \frac { 5 } { 6 } , 1 \right\}$ 
B)  $\left\{ - \frac { 5 } { 6 } , 0,1 \right\}$ 
C)  $\left\{ - \frac { 6 } { 5 } , 0,1 \right\}$ 
D)  $\left\{ - 1,0 , \frac { 5 } { 6 } \right\}$ 
A)  $\left\{ - \frac { 5 } { 6 } , 1 \right\}$ 
B)  $\left\{ - \frac { 5 } { 6 } , 0,1 \right\}$ 
C)  $\left\{ - \frac { 6 } { 5 } , 0,1 \right\}$ 
D)  $\left\{ - 1,0 , \frac { 5 } { 6 } \right\}$

Question 4

Evaluate the polynomial function.
-If $f ( x ) = x ^ { 2 } + 6 x$, find $f ( a )$.

Accepted Answer

A)  $x ^ { 2 } + a x$ 
B)  $a x ^ { 2 } + 6 a x$ 
C)  $6 a$ 
D)  $a ^ { 2 } + 6 a$ 
A)  $x ^ { 2 } + a x$ 
B)  $a x ^ { 2 } + 6 a x$ 
C)  $6 a$ 
D)  $a ^ { 2 } + 6 a$

Question 5

Factor.
-$$x ^ { 2 } + 8 x + 16$$

Accepted Answer

A)  $( x + 4 ) ( x - 4 )$ 
B)  $( x + 4 ) ^ { 2 }$ 
C)  $( x - 4 ) ^ { 2 }$ 
D)  prime polynomial 
A)  $( x + 4 ) ( x - 4 )$ 
B)  $( x + 4 ) ^ { 2 }$ 
C)  $( x - 4 ) ^ { 2 }$ 
D)  prime polynomial

Question 6

Perform the indicated operation.
-$$( 3 a - 8 b ) ( 3 a + 8 b )$$

Accepted Answer

A)  $9 a ^ { 2 } - 64 b ^ { 2 }$ 
B)  $6 a ^ { 2 } - 48 a ^ { 2 } - 16 b ^ { 2 }$ 
C)  $6 a ^ { 2 } - 16 b ^ { 2 }$ 
D)  $9 a ^ { 2 } - 48 a b - 64 b ^ { 2 }$ 
A)  $9 a ^ { 2 } - 64 b ^ { 2 }$ 
B)  $6 a ^ { 2 } - 48 a ^ { 2 } - 16 b ^ { 2 }$ 
C)  $6 a ^ { 2 } - 16 b ^ { 2 }$ 
D)  $9 a ^ { 2 } - 48 a b - 64 b ^ { 2 }$

Question 7

Multiply.
-$$[ 8 y + ( 8 x + 5 ) ] [ 8 y - ( 8 x + 5 ) ]$$

Accepted Answer

A)  $64 y ^ { 2 } - 64 x ^ { 2 } - 80 x + 25$ 
B)  $64 y ^ { 2 } - 64 x ^ { 2 } + 80 x + 25$ 
C)  $64 y ^ { 2 } - 64 x ^ { 2 } - 40 x - 25$ 
D)  $64 y ^ { 2 } - 64 x ^ { 2 } - 80 x - 25$ 
A)  $64 y ^ { 2 } - 64 x ^ { 2 } - 80 x + 25$ 
B)  $64 y ^ { 2 } - 64 x ^ { 2 } + 80 x + 25$ 
C)  $64 y ^ { 2 } - 64 x ^ { 2 } - 40 x - 25$ 
D)  $64 y ^ { 2 } - 64 x ^ { 2 } - 80 x - 25$

Question 8

Multiply.
-$$( 8 y + x ) ( 8 y - x )$$

Accepted Answer

A)  $64 y ^ { 2 } - x ^ { 2 }$ 
B)  $64 y ^ { 2 } + 16 x y - x ^ { 2 }$ 
C)  $16 y ^ { 2 } - x ^ { 2 }$ 
D)  $64 y ^ { 2 } - 16 x y - x ^ { 2 }$ 
A)  $64 y ^ { 2 } - x ^ { 2 }$ 
B)  $64 y ^ { 2 } + 16 x y - x ^ { 2 }$ 
C)  $16 y ^ { 2 } - x ^ { 2 }$ 
D)  $64 y ^ { 2 } - 16 x y - x ^ { 2 }$

Question 9

Find the GCF of the list of monomials.
-$8 x ^ { 3 } y ^ { 4 } , 8 x ^ { 5 } y ^ { 3 } , 2 x ^ { 4 } y ^ { 2 }$

Accepted Answer

A)  $8 x ^ { 3 } y ^ { 2 }$ 
B)  $2 x ^ { 3 } y ^ { 2 }$ 
C)  $4 \mathrm { x } ^ { 5 } \mathrm { y } ^ { 4 }$ 
D)  $2 x ^ { 2 } y ^ { 3 }$ 
A)  $8 x ^ { 3 } y ^ { 2 }$ 
B)  $2 x ^ { 3 } y ^ { 2 }$ 
C)  $4 \mathrm { x } ^ { 5 } \mathrm { y } ^ { 4 }$ 
D)  $2 x ^ { 2 } y ^ { 3 }$

Question 10

Factor the trinomial.
-$9 x ^ { 2 } - 42 x + 49$

Accepted Answer

A)  $( 9 x + 1 ) ( x + 49 )$ 
B)  $( 3 x + 7 ) ^ { 2 }$ 
C)  $( 3 x - 7 ) ( 3 x + 7 )$ 
D)  $( 3 x - 7 ) ^ { 2 }$ 
A)  $( 9 x + 1 ) ( x + 49 )$ 
B)  $( 3 x + 7 ) ^ { 2 }$ 
C)  $( 3 x - 7 ) ( 3 x + 7 )$ 
D)  $( 3 x - 7 ) ^ { 2 }$

Question 11

Multiply.
-$$\left( x ^ { 2 } + 4 y \right) \left( x ^ { 2 } - 4 y \right)$$

Accepted Answer

A)  $x ^ { 4 } - 16 y ^ { 2 }$ 
B)  $x ^ { 4 } - 8 y ^ { 2 }$ 
C)  $x ^ { 4 } + 8 x ^ { 2 } y - 16 y ^ { 2 }$ 
D)  $x ^ { 4 } - 8 x ^ { 2 } y - 16 y ^ { 2 }$ 
A)  $x ^ { 4 } - 16 y ^ { 2 }$ 
B)  $x ^ { 4 } - 8 y ^ { 2 }$ 
C)  $x ^ { 4 } + 8 x ^ { 2 } y - 16 y ^ { 2 }$ 
D)  $x ^ { 4 } - 8 x ^ { 2 } y - 16 y ^ { 2 }$

Question 12

Factor the trinomial.
-$$4 x ^ { 2 } + x - 105$$

Accepted Answer

A)  $( 4 x - 21 ) ( x + 5 )$ 
B)  $( 4 x - 5 ) ( x + 21 )$ 
C)  $( 4 x + 21 ) ( x - 5 )$ 
D)  $( 4 x + 5 ) ( x - 21 )$ 
A)  $( 4 x - 21 ) ( x + 5 )$ 
B)  $( 4 x - 5 ) ( x + 21 )$ 
C)  $( 4 x + 21 ) ( x - 5 )$ 
D)  $( 4 x + 5 ) ( x - 21 )$

Question 13

Factor the polynomial.
-$$x ^ { 2 } + 5 x - 50$$

Accepted Answer

A)  $( x - 10 ) ( x + 1 )$ 
B)  $( x + 10 ) ( x - 5 )$ 
C)  $( x - 10 ) ( x + 5 )$ 
D)  prime polynomial 
A)  $( x - 10 ) ( x + 1 )$ 
B)  $( x + 10 ) ( x - 5 )$ 
C)  $( x - 10 ) ( x + 5 )$ 
D)  prime polynomial

Question 14

Solve.
-Kara is making a box by cutting out 2 -in.-by-2-in. squares from a square piece of cardboard and folding the edges to make a 2-inch-high box. What size of cardboard does Kara need to make a 2-inch-high box with a volume of 8 cubic inches?

Accepted Answer

A)  6 in. by 6 in. 
B)  4 in. by 4 in. 
C)  2 in. by 2 in. 
D)  $10 \mathrm { in }$. by $10 \mathrm { in }$. 
A)  6 in. by 6 in. 
B)  4 in. by 4 in. 
C)  2 in. by 2 in. 
D)  $10 \mathrm { in }$. by $10 \mathrm { in }$.

Question 15

For the given f(x $$f ( x ) \text { and } g ( x ) \text {, find } \frac { f ( x ) } { g ( x ) } \text {. Also find any x-values that are not in the domain of } \frac { f ( x ) } { g ( x ) } \text {. }$$
-$$f ( x ) = 18 x ^ { 2 } - 24 x + 12 ; g ( x ) = 6 x$$

Accepted Answer

A)  $5 x - 4 ; x \neq 0$ 
B)  $3 x - 4 ; x \neq 0$ 
C)  $3 x - 4 + \frac { 2 } { x } ; x \neq 6$ 
D)  $3 x - 4 + \frac { 2 } { x } ; x \neq 0$ 
A)  $5 x - 4 ; x \neq 0$ 
B)  $3 x - 4 ; x \neq 0$ 
C)  $3 x - 4 + \frac { 2 } { x } ; x \neq 6$ 
D)  $3 x - 4 + \frac { 2 } { x } ; x \neq 0$

Question 16

Multiply.
-$$( x + 3 ) ^ { 2 }$$

Accepted Answer

A)  $9 x ^ { 2 } + 6 x + 9$ 
B)  $x ^ { 2 } + 6 x + 9$ 
C)  $x + 9$ 
D)  $x ^ { 2 } + 9$ 
A)  $9 x ^ { 2 } + 6 x + 9$ 
B)  $x ^ { 2 } + 6 x + 9$ 
C)  $x + 9$ 
D)  $x ^ { 2 } + 9$

Question 17

Write the area of the shaded region as a factored polynomial.
-

Accepted Answer

A)  $x ^ { 2 } - 144 y ^ { 2 }$ 
B)  $x ^ { 2 } + 144 y ^ { 2 }$ 
C)  $( x - 12 y ) ^ { 2 }$ 
D)  $( x + 12 y ) ( x - 12 y )$ 
A)  $x ^ { 2 } - 144 y ^ { 2 }$ 
B)  $x ^ { 2 } + 144 y ^ { 2 }$ 
C)  $( x - 12 y ) ^ { 2 }$ 
D)  $( x + 12 y ) ( x - 12 y )$

Question 18

Solve the equation.
-$$25 x ^ { 2 } + 30 x + 9 = 0$$

Accepted Answer

A)  $\left\{ - \frac { 3 } { 5 } \right\}$ 
B)  $\left\{ - \frac { 5 } { 3 } , 0 \right\}$ 
C)  $\left\{ - \frac { 3 } { 5 } , 0 \right\}$ 
D)  $\left\{ - \frac { 5 } { 3 } \right\}$ 
A)  $\left\{ - \frac { 3 } { 5 } \right\}$ 
B)  $\left\{ - \frac { 5 } { 3 } , 0 \right\}$ 
C)  $\left\{ - \frac { 3 } { 5 } , 0 \right\}$ 
D)  $\left\{ - \frac { 5 } { 3 } \right\}$

Question 19

Perform the indicated operation.
-$$( 9 x - 1 ) \left( x ^ { 2 } - 7 x + 1 \right)$$

Accepted Answer

A)  $9 x ^ { 3 } - 62 x ^ { 2 } + 2 x - 1$ 
B)  $9 x ^ { 3 } - 63 x ^ { 2 } + 9 x + 1$ 
C)  $9 x ^ { 3 } + 64 x ^ { 2 } - 16 x + 1$ 
D)  $9 x ^ { 3 } - 64 x ^ { 2 } + 16 x - 1$ 
A)  $9 x ^ { 3 } - 62 x ^ { 2 } + 2 x - 1$ 
B)  $9 x ^ { 3 } - 63 x ^ { 2 } + 9 x + 1$ 
C)  $9 x ^ { 3 } + 64 x ^ { 2 } - 16 x + 1$ 
D)  $9 x ^ { 3 } - 64 x ^ { 2 } + 16 x - 1$

Question 20

Simplify the polynomial by combining like terms.
-$$\left( 12 x ^ { 2 } y - 9 x y + 7 \right) + \left( - 11 x ^ { 2 } y + 5 x y - 8 \right)$$

Accepted Answer

A)  $23 x ^ { 2 } y + 14 x y + 15$ 
B)  $- x ^ { 2 } y - 14 x y + 15$ 
C)  $- 4 x ^ { 3 } y ^ { 2 } - 1$ 
D)  $x ^ { 2 } y - 4 x y - 1$ 
A)  $23 x ^ { 2 } y + 14 x y + 15$ 
B)  $- x ^ { 2 } y - 14 x y + 15$ 
C)  $- 4 x ^ { 3 } y ^ { 2 } - 1$ 
D)  $x ^ { 2 } y - 4 x y - 1$

Factor. - $25 y ^ { 2 } - 49$

Factor out the greatest common factor. - $32 x ^ { 5 } y + 28 x y ^ { 4 }$

Solve the equation. - $x ( 6 x + 5 ) ( x - 1 ) = 0$

Evaluate the polynomial function. -If $f ( x ) = x ^ { 2 } + 6 x$ , find $f ( a )$ .

Factor. - $x ^ { 2 } + 8 x + 16$

Perform the indicated operation. - $( 3 a - 8 b ) ( 3 a + 8 b )$

Multiply. - $[ 8 y + ( 8 x + 5 ) ] [ 8 y - ( 8 x + 5 ) ]$

Multiply. - $( 8 y + x ) ( 8 y - x )$

Find the GCF of the list of monomials. - $8 x ^ { 3 } y ^ { 4 } , 8 x ^ { 5 } y ^ { 3 } , 2 x ^ { 4 } y ^ { 2 }$

Factor the trinomial. - $9 x ^ { 2 } - 42 x + 49$

Multiply. - $\left( x ^ { 2 } + 4 y \right) \left( x ^ { 2 } - 4 y \right)$

Factor the trinomial. - $4 x ^ { 2 } + x - 105$

Factor the polynomial. - $x ^ { 2 } + 5 x - 50$

Solve. -Kara is making a box by cutting out 2 -in.-by-2-in. squares from a square piece of cardboard and folding the edges to make a 2-inch-high box. What size of cardboard does Kara need to make a 2-inch-high box with a volume of 8 cubic inches?

For the given f(x $f ( x ) \text { and } g ( x ) \text {, find } \frac { f ( x ) } { g ( x ) } \text {. Also find any x-values that are not in the domain of } \frac { f ( x ) } { g ( x ) } \text {. }$ - $f ( x ) = 18 x ^ { 2 } - 24 x + 12 ; g ( x ) = 6 x$

Multiply. - $( x + 3 ) ^ { 2 }$

Write the area of the shaded region as a factored polynomial. -

Solve the equation. - $25 x ^ { 2 } + 30 x + 9 = 0$

Perform the indicated operation. - $( 9 x - 1 ) \left( x ^ { 2 } - 7 x + 1 \right)$

Simplify the polynomial by combining like terms. - $\left( 12 x ^ { 2 } y - 9 x y + 7 \right) + \left( - 11 x ^ { 2 } y + 5 x y - 8 \right)$

Real Numbers and Algebraic Expressions

Equations, Inequalities, and Problem Solving

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Exam 5: Polynomials and Polynomial Functions

Factor. - 25y2−4925 y ^ { 2 } - 4925y2−49

Factor out the greatest common factor. - 32x5y+28xy432 x ^ { 5 } y + 28 x y ^ { 4 }32x5y+28xy4

Solve the equation. - x(6x+5)(x−1)=0x ( 6 x + 5 ) ( x - 1 ) = 0x(6x+5)(x−1)=0

Evaluate the polynomial function. -If f(x)=x2+6xf ( x ) = x ^ { 2 } + 6 xf(x)=x2+6x , find f(a)f ( a )f(a) .

Factor. - x2+8x+16x ^ { 2 } + 8 x + 16x2+8x+16

Perform the indicated operation. - (3a−8b)(3a+8b)( 3 a - 8 b ) ( 3 a + 8 b )(3a−8b)(3a+8b)

Multiply. - [8y+(8x+5)][8y−(8x+5)][ 8 y + ( 8 x + 5 ) ] [ 8 y - ( 8 x + 5 ) ][8y+(8x+5)][8y−(8x+5)]

Multiply. - (8y+x)(8y−x)( 8 y + x ) ( 8 y - x )(8y+x)(8y−x)

Find the GCF of the list of monomials. - 8x3y4,8x5y3,2x4y28 x ^ { 3 } y ^ { 4 } , 8 x ^ { 5 } y ^ { 3 } , 2 x ^ { 4 } y ^ { 2 }8x3y4,8x5y3,2x4y2

Factor the trinomial. - 9x2−42x+499 x ^ { 2 } - 42 x + 499x2−42x+49

Multiply. - (x2+4y)(x2−4y)\left( x ^ { 2 } + 4 y \right) \left( x ^ { 2 } - 4 y \right)(x2+4y)(x2−4y)

Factor the trinomial. - 4x2+x−1054 x ^ { 2 } + x - 1054x2+x−105

Factor the polynomial. - x2+5x−50x ^ { 2 } + 5 x - 50x2+5x−50