Question 1

Determine which factoring technique is appropriate for the given polynomial.
-$x^{2}+8 x+12$

Accepted Answer

A)  factoring by grouping 
B)  factor out GCF 
C)  trinomial, leading coefficient of 1 
D)  trinomial, leading coefficient other than 1 
A)  factoring by grouping 
B)  factor out GCF 
C)  trinomial, leading coefficient of 1 
D)  trinomial, leading coefficient other than 1

Question 2

Factor completely. If the polynomial cannot be factored, write "prime."
-$250 k^{3} m-16 m^{4}$

Accepted Answer

A)  $2 \mathrm{~m}(5 \mathrm{k}-2 \mathrm{~m})\left(25 \mathrm{k}^{2}+10 \mathrm{~km}+4 \mathrm{~m}^{2}\right)$ 
B)  $\left(10 \mathrm{~km}-4 \mathrm{~m}^{2}\right)\left(25 \mathrm{k}^{2}+4 \mathrm{~m}^{2}\right)$ 
C)  $2 \mathrm{~m}\left(5 \mathrm{k}+2 \mathrm{~m}^{2}\right)\left(25 \mathrm{k}^{2}-10 \mathrm{~km}+4 \mathrm{~km}^{2}\right)$ 
D)  $2 \mathrm{~m}(125 \mathrm{k}-2 \mathrm{~m})\left(\mathrm{k}^{2}+10 \mathrm{~km}+4 \mathrm{~m}^{2}\right)$ 
A)  $2 \mathrm{~m}(5 \mathrm{k}-2 \mathrm{~m})\left(25 \mathrm{k}^{2}+10 \mathrm{~km}+4 \mathrm{~m}^{2}\right)$ 
B)  $\left(10 \mathrm{~km}-4 \mathrm{~m}^{2}\right)\left(25 \mathrm{k}^{2}+4 \mathrm{~m}^{2}\right)$ 
C)  $2 \mathrm{~m}\left(5 \mathrm{k}+2 \mathrm{~m}^{2}\right)\left(25 \mathrm{k}^{2}-10 \mathrm{~km}+4 \mathrm{~km}^{2}\right)$ 
D)  $2 \mathrm{~m}(125 \mathrm{k}-2 \mathrm{~m})\left(\mathrm{k}^{2}+10 \mathrm{~km}+4 \mathrm{~m}^{2}\right)$

Question 3

Factor the GCF out of the given expression.
-$x^{8}-20 x^{3}$

Accepted Answer

A)  $x\left(x^{7}-20 x^{2}\right)$ 
B)  $x^{3}\left(x^{5}+20\right)$ 
C)  $x^{3}\left(x^{5}-20\right)$ 
D)  $x^{5}\left(x^{3}-20\right)$ 
A)  $x\left(x^{7}-20 x^{2}\right)$ 
B)  $x^{3}\left(x^{5}+20\right)$ 
C)  $x^{3}\left(x^{5}-20\right)$ 
D)  $x^{5}\left(x^{3}-20\right)$

Question 4

Factor completely. If the polynomial cannot be factored, write "prime."
-$x^{2}-22 x y+120 y^{2}$

Accepted Answer

A)  $(\mathrm{x}+12 \mathrm{y})(\mathrm{x}-10 \mathrm{y})$ 
B)  $(\mathrm{x}-12 \mathrm{y})(\mathrm{x}-10 \mathrm{y})$ 
C)  $(x-120 y)(x-y)$ 
D)  Prime 
A)  $(\mathrm{x}+12 \mathrm{y})(\mathrm{x}-10 \mathrm{y})$ 
B)  $(\mathrm{x}-12 \mathrm{y})(\mathrm{x}-10 \mathrm{y})$ 
C)  $(x-120 y)(x-y)$ 
D)  Prime

Question 5

$\left(6 x^{2} y-4 x+5 y^{2}\right)+\left(5 x^{2} y-4 x+6 y^{2}\right)$

Accepted Answer

A)  $30 x^{2} y-4 x+11 y^{2}$ 
B)  $11 x^{4} y-8 x^{2}+11 y^{2}$ 
C)  $11 x^{2} y-4 x+11 y^{2}$ 
D)  $11 x^{2} y-8 x+11 y^{2}$ 
A)  $30 x^{2} y-4 x+11 y^{2}$ 
B)  $11 x^{4} y-8 x^{2}+11 y^{2}$ 
C)  $11 x^{2} y-4 x+11 y^{2}$ 
D)  $11 x^{2} y-8 x+11 y^{2}$

Question 6

Factor completely. If the polynomial cannot be factored, write "prime."
-$x^{2}+3 x y-208 y^{2}$

Accepted Answer

A)  $(x-16 y)(x+y)$ 
B)  $(x-16 y)(x+13 y)$ 
C)  $(x+16 y)(x-13 y)$ 
D)  $(x-y)(x+13 y)$ 
A)  $(x-16 y)(x+y)$ 
B)  $(x-16 y)(x+13 y)$ 
C)  $(x+16 y)(x-13 y)$ 
D)  $(x-y)(x+13 y)$

Question 7

$\mathrm{x}(3 \mathrm{x}+6)=0$

Accepted Answer

A)  $\left\{0, \frac{1}{2}\right\}$ 
B)  $\{0,2\}$ 
C)  $\{0,-2\}$ 
D)  $\left\{0,-\frac{1}{2}\right\}$ 
A)  $\left\{0, \frac{1}{2}\right\}$ 
B)  $\{0,2\}$ 
C)  $\{0,-2\}$ 
D)  $\left\{0,-\frac{1}{2}\right\}$

Question 8

$\left(3 x^{2} y-5 x y+5 x y^{2}\right)-\left(2 x y-5 x y^{2}+6 x^{2} y\right)$

Accepted Answer

A)  $2 x^{2} y+5 x y^{2}-7 x y$ 
B)  $-3 x^{2} y-10 x y^{2}-3 x y$ 
C)  $-3 x^{2} y+10 x y^{2}-7 x y$ 
D)  $-3 x^{2} y-10 x y^{2}-7 x y$ 
A)  $2 x^{2} y+5 x y^{2}-7 x y$ 
B)  $-3 x^{2} y-10 x y^{2}-3 x y$ 
C)  $-3 x^{2} y+10 x y^{2}-7 x y$ 
D)  $-3 x^{2} y-10 x y^{2}-7 x y$

Question 9

Factor completely. If the polynomial cannot be factored, write "prime."
-$x^{6}-343$

Accepted Answer

A)  $\left(x^{2}+7\right)\left(x^{4}-7 x^{2}+49\right)$ 
B)  $(x-7)\left(x^{5}+7 x+49\right)$ 
C)  $\left(x^{2}-7\right)\left(x^{4}+7 x^{2}+49\right)$ 
D)  $\left(x^{2}-7\right)\left(x^{2}+7 x+49\right)$ 
A)  $\left(x^{2}+7\right)\left(x^{4}-7 x^{2}+49\right)$ 
B)  $(x-7)\left(x^{5}+7 x+49\right)$ 
C)  $\left(x^{2}-7\right)\left(x^{4}+7 x^{2}+49\right)$ 
D)  $\left(x^{2}-7\right)\left(x^{2}+7 x+49\right)$

Question 10

$3 x^{2}-11 x-4=0$

Accepted Answer

A)  $\left\{\frac{1}{11},-\frac{1}{3}\right\}$ 
B)  $\left\{-\frac{1}{3}, 4\right\}$ 
C)  $\left\{-\frac{1}{3}, 3\right\}$ 
D)  $\{-3,4\}$ 
A)  $\left\{\frac{1}{11},-\frac{1}{3}\right\}$ 
B)  $\left\{-\frac{1}{3}, 4\right\}$ 
C)  $\left\{-\frac{1}{3}, 3\right\}$ 
D)  $\{-3,4\}$

Question 11

Factor the GCF out of the given expression.
-$2 \mathrm{a}-6$

Accepted Answer

A)  3(a- 2) 
B)  2(a-6) 
C)  $2(a+3)$ 
D)  $2(a-3)$ 
A)  3(a- 2) 
B)  2(a-6) 
C)  $2(a+3)$ 
D)  $2(a-3)$

Question 12

Evaluate the polynomial or polynomial function for the given value of the variable.
-$3 x^{3}-4 x^{2}-14$ for $x=2$

Accepted Answer

A)  -6 
B)  - 16 
C)  2 
D)  - 18 
A)  -6 
B)  - 16 
C)  2 
D)  - 18

Question 13

Factor completely. If the polynomial cannot be factored, write "prime."
-$4 y^{3}-108$

Accepted Answer

A)  $4(y-3)\left(y^{2}+9\right)$ 
B)  $4(y-3)\left(y^{2}+3 y+9\right)$ 
C)  $(4 y-3)\left(y^{2}+3 y+36\right)$ 
D)  $4(y+3)\left(y^{2}-3 y+9\right)$ 
A)  $4(y-3)\left(y^{2}+9\right)$ 
B)  $4(y-3)\left(y^{2}+3 y+9\right)$ 
C)  $(4 y-3)\left(y^{2}+3 y+36\right)$ 
D)  $4(y+3)\left(y^{2}-3 y+9\right)$

Question 14

Simplify. (A ssume all variables are nonzero.)
-$\frac{4}{70}$

Accepted Answer

A)  1 
B)  0 
C)  4 
D)  $\frac{4}{7}$ 
A)  1 
B)  0 
C)  4 
D)  $\frac{4}{7}$

Question 15

$-6(5 x-8)$

Accepted Answer

A)  $-30 x+48$ 
B)  $30 x-48$ 
C)  $30 x+48$ 
D)  $-30 x-48$ 
A)  $-30 x+48$ 
B)  $30 x-48$ 
C)  $30 x+48$ 
D)  $-30 x-48$

Question 16

Factor the GCF out of the given expression.
-$5 x(3 x-2)-6(3 x-2)$

Accepted Answer

A)  $(3 x-2)(5 x-6)$ 
B)  $(15 x+6)(x+2)$ 
C)  $(3 x+2)(5 x+6)$ 
D)  $(15 x-6)(x-2)$ 
A)  $(3 x-2)(5 x-6)$ 
B)  $(15 x+6)(x+2)$ 
C)  $(3 x+2)(5 x+6)$ 
D)  $(15 x-6)(x-2)$

Question 17

$\left(4 x^{2} y z^{2}-2 x y z-5 x y^{2}\right)-\left(6 x y z+6 x y^{2}+6 x^{2} y z^{2}\right)$

Accepted Answer

A)  $-2 x^{2} y z^{2}+11 x y^{2}+4 x y z$ 
B)  $-8 x^{2} y z^{2}-5 x y^{2}-8 x y z$ 
C)  $-2 x^{2} y z^{2}-11 x y^{2}-8 x y z$ 
D)  $-2 x^{2} y z^{2}+11 x y^{2}-8 x y z$ 
A)  $-2 x^{2} y z^{2}+11 x y^{2}+4 x y z$ 
B)  $-8 x^{2} y z^{2}-5 x y^{2}-8 x y z$ 
C)  $-2 x^{2} y z^{2}-11 x y^{2}-8 x y z$ 
D)  $-2 x^{2} y z^{2}+11 x y^{2}-8 x y z$

Question 18

Rewrite the expression without using negative exponents. (A ssume all variables represent nonzero real numbers.)
-$3 x^{-5}$

Accepted Answer

A)  $\frac{1}{3 x^{5}}$ 
B)  $-2 x$ 
C)  $3 x^{5}$ 
D)  $\frac{3}{x^{5}}$ 
A)  $\frac{1}{3 x^{5}}$ 
B)  $-2 x$ 
C)  $3 x^{5}$ 
D)  $\frac{3}{x^{5}}$

Question 19

The length of a room is 3 feet more than the width. The room has a floor area of 378 square feet. Find the dimensions of the room.

Accepted Answer

A)  Length: 18 feet; Width: 15 feet 
B)  Length: 21 feet; Width: 18 feet 
C)  Length: 24 feet; Width: 21 feet 
D)  Length: 22 feet; Width: 19 feet 
A)  Length: 18 feet; Width: 15 feet 
B)  Length: 21 feet; Width: 18 feet 
C)  Length: 24 feet; Width: 21 feet 
D)  Length: 22 feet; Width: 19 feet

Question 20

Choose the polynomial that has the given factor.
-$3 x+5$

Accepted Answer

A)  $x^{2}-16 x-35$ 
B)  $3 x^{2}-16 x-35$ 
C)  $3 x^{2}+16 x-35$ 
D)  $3 x^{2}+16 x+35$ 
A)  $x^{2}-16 x-35$ 
B)  $3 x^{2}-16 x-35$ 
C)  $3 x^{2}+16 x-35$ 
D)  $3 x^{2}+16 x+35$

Determine which factoring technique is appropriate for the given polynomial. - $x^{2}+8 x+12$

Factor completely. If the polynomial cannot be factored, write "prime." - $250 k^{3} m-16 m^{4}$

Factor the GCF out of the given expression. - $x^{8}-20 x^{3}$

Factor completely. If the polynomial cannot be factored, write "prime." - $x^{2}-22 x y+120 y^{2}$

$\left(6 x^{2} y-4 x+5 y^{2}\right)+\left(5 x^{2} y-4 x+6 y^{2}\right)$

Factor completely. If the polynomial cannot be factored, write "prime." - $x^{2}+3 x y-208 y^{2}$

$\mathrm{x}(3 \mathrm{x}+6)=0$

$\left(3 x^{2} y-5 x y+5 x y^{2}\right)-\left(2 x y-5 x y^{2}+6 x^{2} y\right)$

Factor completely. If the polynomial cannot be factored, write "prime." - $x^{6}-343$

$3 x^{2}-11 x-4=0$

Factor the GCF out of the given expression. - $2 \mathrm{a}-6$

Evaluate the polynomial or polynomial function for the given value of the variable. - $3 x^{3}-4 x^{2}-14$ for $x=2$

Factor completely. If the polynomial cannot be factored, write "prime." - $4 y^{3}-108$

Simplify. (A ssume all variables are nonzero.) - $\frac{4}{70}$

$-6(5 x-8)$

Factor the GCF out of the given expression. - $5 x(3 x-2)-6(3 x-2)$

$\left(4 x^{2} y z^{2}-2 x y z-5 x y^{2}\right)-\left(6 x y z+6 x y^{2}+6 x^{2} y z^{2}\right)$

Rewrite the expression without using negative exponents. (A ssume all variables represent nonzero real numbers.) - $3 x^{-5}$

The length of a room is 3 feet more than the width. The room has a floor area of 378 square feet. Find the dimensions of the room.

Choose the polynomial that has the given factor. - $3 x+5$

Review of Real Numbers

Linear and Absolute Value Equations and Inequalities

Graphing Linear Equations

Systems of Equations

Rational Expressions and Equations

Radical Expressions and Equations

Quadratic Equations

Logarithmic and Exponential Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 5: Exponents, Polynomials, and Factoring Polynomials

Determine which factoring technique is appropriate for the given polynomial. - x2+8x+12x^{2}+8 x+12x2+8x+12

Factor completely. If the polynomial cannot be factored, write "prime." - 250k3m−16m4250 k^{3} m-16 m^{4}250k3m−16m4

Factor the GCF out of the given expression. - x8−20x3x^{8}-20 x^{3}x8−20x3

Factor completely. If the polynomial cannot be factored, write "prime." - x2−22xy+120y2x^{2}-22 x y+120 y^{2}x2−22xy+120y2

(6x2y−4x+5y2)+(5x2y−4x+6y2)\left(6 x^{2} y-4 x+5 y^{2}\right)+\left(5 x^{2} y-4 x+6 y^{2}\right)(6x2y−4x+5y2)+(5x2y−4x+6y2)

Factor completely. If the polynomial cannot be factored, write "prime." - x2+3xy−208y2x^{2}+3 x y-208 y^{2}x2+3xy−208y2

x(3x+6)=0\mathrm{x}(3 \mathrm{x}+6)=0x(3x+6)=0

(3x2y−5xy+5xy2)−(2xy−5xy2+6x2y)\left(3 x^{2} y-5 x y+5 x y^{2}\right)-\left(2 x y-5 x y^{2}+6 x^{2} y\right)(3x2y−5xy+5xy2)−(2xy−5xy2+6x2y)

Factor completely. If the polynomial cannot be factored, write "prime." - x6−343x^{6}-343x6−343

3x2−11x−4=03 x^{2}-11 x-4=03x2−11x−4=0

Factor the GCF out of the given expression. - 2a−62 \mathrm{a}-62a−6

Evaluate the polynomial or polynomial function for the given value of the variable. - 3x3−4x2−143 x^{3}-4 x^{2}-143x3−4x2−14 for x=2x=2x=2

Factor completely. If the polynomial cannot be factored, write "prime." - 4y3−1084 y^{3}-1084y3−108

Simplify. (A ssume all variables are nonzero.) - 470\frac{4}{70}704​

−6(5x−8)-6(5 x-8)−6(5x−8)

Factor the GCF out of the given expression. - 5x(3x−2)−6(3x−2)5 x(3 x-2)-6(3 x-2)5x(3x−2)−6(3x−2)

(4x2yz2−2xyz−5xy2)−(6xyz+6xy2+6x2yz2)\left(4 x^{2} y z^{2}-2 x y z-5 x y^{2}\right)-\left(6 x y z+6 x y^{2}+6 x^{2} y z^{2}\right)(4x2yz2−2xyz−5xy2)−(6xyz+6xy2+6x2yz2)

Rewrite the expression without using negative exponents. (A ssume all variables represent nonzero real numbers.) - 3x−53 x^{-5}3x−5

The length of a room is 3 feet more than the width. The room has a floor area of 378 square feet. Find the dimensions of the room.

Choose the polynomial that has the given factor. - 3x+53 x+53x+5

Review of Real Numbers

Linear and Absolute Value Equations and Inequalities

Graphing Linear Equations

Systems of Equations

Rational Expressions and Equations

Radical Expressions and Equations

Quadratic Equations

Logarithmic and Exponential Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Determine which factoring technique is appropriate for the given polynomial. - $x^{2}+8 x+12$

Factor completely. If the polynomial cannot be factored, write "prime." - $250 k^{3} m-16 m^{4}$

Factor the GCF out of the given expression. - $x^{8}-20 x^{3}$

Factor completely. If the polynomial cannot be factored, write "prime." - $x^{2}-22 x y+120 y^{2}$

$\left(6 x^{2} y-4 x+5 y^{2}\right)+\left(5 x^{2} y-4 x+6 y^{2}\right)$

Factor completely. If the polynomial cannot be factored, write "prime." - $x^{2}+3 x y-208 y^{2}$

$\mathrm{x}(3 \mathrm{x}+6)=0$

$\left(3 x^{2} y-5 x y+5 x y^{2}\right)-\left(2 x y-5 x y^{2}+6 x^{2} y\right)$

Factor completely. If the polynomial cannot be factored, write "prime." - $x^{6}-343$

$3 x^{2}-11 x-4=0$

Factor the GCF out of the given expression. - $2 \mathrm{a}-6$

Evaluate the polynomial or polynomial function for the given value of the variable. - $3 x^{3}-4 x^{2}-14$ for $x=2$

Factor completely. If the polynomial cannot be factored, write "prime." - $4 y^{3}-108$

Simplify. (A ssume all variables are nonzero.) - $\frac{4}{70}$

$-6(5 x-8)$

Factor the GCF out of the given expression. - $5 x(3 x-2)-6(3 x-2)$

$\left(4 x^{2} y z^{2}-2 x y z-5 x y^{2}\right)-\left(6 x y z+6 x y^{2}+6 x^{2} y z^{2}\right)$

Rewrite the expression without using negative exponents. (A ssume all variables represent nonzero real numbers.) - $3 x^{-5}$

Choose the polynomial that has the given factor. - $3 x+5$