Question 1

Divide.
-$\frac { 8 x ^ { 10 } + 6 x ^ { 9 } - 6 x ^ { 7 } + 6 x ^ { 5 } + 5 x ^ { 4 } } { 2 x ^ { 7 } }$

Accepted Answer

A)  $4 x ^ { 3 } + 3 x ^ { 2 } - 3 + \frac { 3 } { x ^ { 2 } } + \frac { 5 } { 2 x ^ { 3 } }$ 
B)  $4 x ^ { 3 } + 6 x ^ { 9 } - 6 x ^ { 7 } + 6 x ^ { 5 } + 5 x ^ { 4 }$ 
C)  $8 x ^ { 10 } + 3 x ^ { 2 } - 3 + \frac { 3 } { x ^ { 2 } } + \frac { 5 } { 2 x ^ { 3 } }$ 
D)  $4 x ^ { 3 } + 3 x ^ { 2 } - 3$ 
A)  $4 x ^ { 3 } + 3 x ^ { 2 } - 3 + \frac { 3 } { x ^ { 2 } } + \frac { 5 } { 2 x ^ { 3 } }$ 
B)  $4 x ^ { 3 } + 6 x ^ { 9 } - 6 x ^ { 7 } + 6 x ^ { 5 } + 5 x ^ { 4 }$ 
C)  $8 x ^ { 10 } + 3 x ^ { 2 } - 3 + \frac { 3 } { x ^ { 2 } } + \frac { 5 } { 2 x ^ { 3 } }$ 
D)  $4 x ^ { 3 } + 3 x ^ { 2 } - 3$

Question 2

13x

Accepted Answer

A)  1 
B)  13 
C)  0 
D)  no degree 
A)  1 
B)  13 
C)  0 
D)  no degree

Question 3

Factor the trinomial.
-$16 x ^ { 2 } - 56 x - 32$

Accepted Answer

A)  $8 ( 2 x + 1 ) ( x - 4 )$ 
B)  $( 16 x - 8 ) ( x + 4 )$ 
C)  $8 ( 2 x - 1 ) ( x + 4 )$ 
D)  prime polynomial 
A)  $8 ( 2 x + 1 ) ( x - 4 )$ 
B)  $( 16 x - 8 ) ( x + 4 )$ 
C)  $8 ( 2 x - 1 ) ( x + 4 )$ 
D)  prime polynomial

Question 4

Subtract.
-$$\left( 5 x ^ { 2 } + 9 x - 4 \right) - \left( - 10 x ^ { 2 } - 3 \right)$$

Accepted Answer

A)  $- 5 x ^ { 2 } + 9 x - 1$ 
B)  $15 x ^ { 2 } + 12 x - 4$ 
C)  $- 5 x ^ { 2 } + 12 x - 4$ 
D)  $15 x ^ { 2 } + 9 x - 1$ 
A)  $- 5 x ^ { 2 } + 9 x - 1$ 
B)  $15 x ^ { 2 } + 12 x - 4$ 
C)  $- 5 x ^ { 2 } + 12 x - 4$ 
D)  $15 x ^ { 2 } + 9 x - 1$

Question 5

Factor the polynomial.
-$$14 x ^ { 6 } + 8 x ^ { 4 } + 16 x ^ { 2 }$$

Accepted Answer

A)  $2 \left( 7 x ^ { 6 } + 4 x ^ { 4 } + 8 x ^ { 2 } \right)$ 
B)  $2 x ^ { 2 } \left( 7 x ^ { 4 } + 4 x ^ { 2 } + 8 \right)$ 
C)  $2 x \left( 7 x ^ { 4 } + 4 x ^ { 2 } + 8 \right)$ 
D)  $x ^ { 2 } \left( 14 x ^ { 4 } + 8 x ^ { 2 } + 16 \right)$ 
A)  $2 \left( 7 x ^ { 6 } + 4 x ^ { 4 } + 8 x ^ { 2 } \right)$ 
B)  $2 x ^ { 2 } \left( 7 x ^ { 4 } + 4 x ^ { 2 } + 8 \right)$ 
C)  $2 x \left( 7 x ^ { 4 } + 4 x ^ { 2 } + 8 \right)$ 
D)  $x ^ { 2 } \left( 14 x ^ { 4 } + 8 x ^ { 2 } + 16 \right)$

Question 6

Divide.
-$$\frac { y ^ { 3 } - 125 } { y - 5 }$$

Accepted Answer

A)  $y ^ { 2 } - 5 y + 25$ 
B)  $y ^ { 2 } + 5 y + 25$ 
C)  $y ^ { 2 } + 25$ 
D)  $y ^ { 2 } + 5 y - 25$ 
A)  $y ^ { 2 } - 5 y + 25$ 
B)  $y ^ { 2 } + 5 y + 25$ 
C)  $y ^ { 2 } + 25$ 
D)  $y ^ { 2 } + 5 y - 25$

Question 7

Find the function.
-If $P ( x ) = 6 x - 8$, find $P ( - x )$.

Accepted Answer

A)  $2 x$ 
B)  $6 x + 8$ 
C)  $- 6 x - 8$ 
D)  $- 6 x + 8$ 
A)  $2 x$ 
B)  $6 x + 8$ 
C)  $- 6 x - 8$ 
D)  $- 6 x + 8$

Question 8

Factor the polynomial completely.
-$$x ^ { 2 } y - 49 y - x ^ { 2 } + 49$$

Accepted Answer

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

Question 9

Factor.
-$$49 x ^ { 3 } y - 42 x ^ { 2 } y ^ { 2 } + 9 x y ^ { 3 }$$

Accepted Answer

A)  $x y ( 7 x - 3 y ) ^ { 2 }$ 
B)  $\left( 49 x ^ { 2 } y + x y \right) \left( x + 9 y ^ { 2 } \right)$ 
C)  $x y ( 7 x - 3 y ) ( 7 x + 3 y )$ 
D)  $x y ( 7 x + 3 y ) ^ { 2 }$ 
A)  $x y ( 7 x - 3 y ) ^ { 2 }$ 
B)  $\left( 49 x ^ { 2 } y + x y \right) \left( x + 9 y ^ { 2 } \right)$ 
C)  $x y ( 7 x - 3 y ) ( 7 x + 3 y )$ 
D)  $x y ( 7 x + 3 y ) ^ { 2 }$

Question 10

Fill in the blank with one of the words or phrases listed below.

-A is a polynomial with one term.

Accepted Answer

A)  monomial 
B)  trinomial 
C)  binomial 
D)  quadratic equation 
A)  monomial 
B)  trinomial 
C)  binomial 
D)  quadratic equation

Question 11

Solve.
-The force in newtons needed to stretch a certain spring $x$ centimeters from its resting position is given by the polynomial function $f ( x ) = 6 x ^ { 2 }$, where 6 is the spring constant. If a force of 150 newtons is applied, how far will the spring be stretched?

Accepted Answer

A)  $5 \mathrm {~cm}$ 
B)  $25 \mathrm {~cm}$ 
C)  $30 \mathrm {~cm}$ 
D)  $6 \mathrm {~cm}$ 
A)  $5 \mathrm {~cm}$ 
B)  $25 \mathrm {~cm}$ 
C)  $30 \mathrm {~cm}$ 
D)  $6 \mathrm {~cm}$

Question 12

Factor.
-$216 y ^ { 3 } + 343$

Accepted Answer

A)  $( 6 y + 7 ) \left( 36 y ^ { 2 } - 42 y + 49 \right)$ 
B)  $( 216 y - 7 ) \left( y ^ { 2 } + 42 y + 49 \right)$ 
C)  $( 6 y + 7 ) \left( 36 y ^ { 2 } + 42 y + 49 \right)$ 
D)  $( 6 y - 7 ) \left( 36 y ^ { 2 } + 42 y + 49 \right)$ 
A)  $( 6 y + 7 ) \left( 36 y ^ { 2 } - 42 y + 49 \right)$ 
B)  $( 216 y - 7 ) \left( y ^ { 2 } + 42 y + 49 \right)$ 
C)  $( 6 y + 7 ) \left( 36 y ^ { 2 } + 42 y + 49 \right)$ 
D)  $( 6 y - 7 ) \left( 36 y ^ { 2 } + 42 y + 49 \right)$

Question 13

Simplify the polynomial by combining like terms.
-$$3 x ^ { 9 } + 11 x ^ { 4 } + 13 x ^ { 9 } + 3 x ^ { 9 } - 1 x ^ { 4 }$$

Accepted Answer

A)  $19 x ^ { 9 } + 10 x ^ { 4 }$ 
B)  $29 \mathrm { x } ^ { 9 }$ 
C)  $3 x ^ { 9 } + 11 x ^ { 4 } + 13 x ^ { 9 } + 3 x ^ { 9 } - 1 x ^ { 4 }$ 
D)  $29 x ^ { 9 } + 29 x ^ { 4 }$ 
A)  $19 x ^ { 9 } + 10 x ^ { 4 }$ 
B)  $29 \mathrm { x } ^ { 9 }$ 
C)  $3 x ^ { 9 } + 11 x ^ { 4 } + 13 x ^ { 9 } + 3 x ^ { 9 } - 1 x ^ { 4 }$ 
D)  $29 x ^ { 9 } + 29 x ^ { 4 }$

Question 14

Solve the equation for the variable.
-$$3 x ^ { 3 } + 5 x ^ { 2 } = 27 x + 45$$

Accepted Answer

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

Question 15

Divide.
-$$\left( 12 x ^ { 3 } + 27 x ^ { 2 } + 31 x + 20 \right) \div ( - 4 x - 5 )$$

Accepted Answer

A)  $x ^ { 2 } - 3 x - 4$ 
B)  $- 3 x ^ { 2 } - 3 x - 4$ 
C)  $x ^ { 2 } + 3 x + 4$ 
D)  $- 3 x ^ { 2 } - 4$ 
A)  $x ^ { 2 } - 3 x - 4$ 
B)  $- 3 x ^ { 2 } - 3 x - 4$ 
C)  $x ^ { 2 } + 3 x + 4$ 
D)  $- 3 x ^ { 2 } - 4$

Question 16

Factor out the greatest common factor.
-$$15 a ( a - b ) + ( a - b )$$

Accepted Answer

A)  $16 a ( a - b )$ 
B)  $15 a ( a - b )$ 
C)  $( a - b ) ( 15 a + 1 )$ 
D)  $\left( 15 a ^ { 2 } - 15 a b \right) + ( a - b )$ 
A)  $16 a ( a - b )$ 
B)  $15 a ( a - b )$ 
C)  $( a - b ) ( 15 a + 1 )$ 
D)  $\left( 15 a ^ { 2 } - 15 a b \right) + ( a - b )$

Question 17

Factor. Assume that variables used as exponents represent positive integers.
-$$x ^ { 2 n } + 11 x ^ { n } + 18$$

Accepted Answer

A)  $\left( x ^ { n } - 9 \right) \left( x ^ { n } + 1 \right)$ 
B)  $\left( x ^ { n } + 9 \right) \left( x ^ { n } + 2 \right)$ 
C)  $\left( x ^ { n } - 9 \right) \left( x ^ { n } + 2 \right)$ 
D)  prime polynomial 
A)  $\left( x ^ { n } - 9 \right) \left( x ^ { n } + 1 \right)$ 
B)  $\left( x ^ { n } + 9 \right) \left( x ^ { n } + 2 \right)$ 
C)  $\left( x ^ { n } - 9 \right) \left( x ^ { n } + 2 \right)$ 
D)  prime polynomial

Question 18

Fill in the blank with one of the words or phrases listed below.

-is the process of writing a polynomial as a product.

Accepted Answer

A)  Synthetic division 
B)  FOIL 
C)  Factoring 
D)  Degree of a polynomial 
A)  Synthetic division 
B)  FOIL 
C)  Factoring 
D)  Degree of a polynomial

Question 19

Factor completely.
-$$( x + y ) ^ { 3 } + 343$$

Accepted Answer

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

Question 20

Simplify the polynomial by combining like terms.
-$$- 15 x ^ { 9 } + 4 x ^ { 6 } + x ^ { 9 } + 6 x ^ { 9 }$$

Accepted Answer

A)  $- 4 x 18$ 
B)  $- 8 x ^ { 9 } + 4 x ^ { 6 }$ 
C)  $- 4 x ^ { 9 } - 4 x ^ { 6 }$ 
D)  $- 15 x ^ { 9 } + 4 x ^ { 6 } + x ^ { 9 } + 6 x ^ { 9 }$ 
A)  $- 4 x 18$ 
B)  $- 8 x ^ { 9 } + 4 x ^ { 6 }$ 
C)  $- 4 x ^ { 9 } - 4 x ^ { 6 }$ 
D)  $- 15 x ^ { 9 } + 4 x ^ { 6 } + x ^ { 9 } + 6 x ^ { 9 }$

Divide. - $\frac { 8 x ^ { 10 } + 6 x ^ { 9 } - 6 x ^ { 7 } + 6 x ^ { 5 } + 5 x ^ { 4 } } { 2 x ^ { 7 } }$

13x

Factor the trinomial. - $16 x ^ { 2 } - 56 x - 32$

Subtract. - $\left( 5 x ^ { 2 } + 9 x - 4 \right) - \left( - 10 x ^ { 2 } - 3 \right)$

Factor the polynomial. - $14 x ^ { 6 } + 8 x ^ { 4 } + 16 x ^ { 2 }$

Divide. - $\frac { y ^ { 3 } - 125 } { y - 5 }$

Find the function. -If $P ( x ) = 6 x - 8$ , find $P ( - x )$ .

Factor the polynomial completely. - $x ^ { 2 } y - 49 y - x ^ { 2 } + 49$

Factor. - $49 x ^ { 3 } y - 42 x ^ { 2 } y ^ { 2 } + 9 x y ^ { 3 }$

Fill in the blank with one of the words or phrases listed below. -A is a polynomial with one term.

Solve. -The force in newtons needed to stretch a certain spring $x$ centimeters from its resting position is given by the polynomial function $f ( x ) = 6 x ^ { 2 }$ , where 6 is the spring constant. If a force of 150 newtons is applied, how far will the spring be stretched?

Factor. - $216 y ^ { 3 } + 343$

Simplify the polynomial by combining like terms. - $3 x ^ { 9 } + 11 x ^ { 4 } + 13 x ^ { 9 } + 3 x ^ { 9 } - 1 x ^ { 4 }$

Solve the equation for the variable. - $3 x ^ { 3 } + 5 x ^ { 2 } = 27 x + 45$

Divide. - $\left( 12 x ^ { 3 } + 27 x ^ { 2 } + 31 x + 20 \right) \div ( - 4 x - 5 )$

Factor out the greatest common factor. - $15 a ( a - b ) + ( a - b )$

Factor. Assume that variables used as exponents represent positive integers. - $x ^ { 2 n } + 11 x ^ { n } + 18$

Fill in the blank with one of the words or phrases listed below. -is the process of writing a polynomial as a product.

Factor completely. - $( x + y ) ^ { 3 } + 343$

Simplify the polynomial by combining like terms. - $- 15 x ^ { 9 } + 4 x ^ { 6 } + x ^ { 9 } + 6 x ^ { 9 }$

Real Numbers and Algebraic Expressions

Equations, Inequalities, and Problem Solving

Graphs and Functions

Systems of Equations and Inequalities

Rational Expressions

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Conic Sections

Fractions

Filters

Exam 5: Polynomials and Polynomial Functions

Divide. - 8x10+6x9−6x7+6x5+5x42x7\frac { 8 x ^ { 10 } + 6 x ^ { 9 } - 6 x ^ { 7 } + 6 x ^ { 5 } + 5 x ^ { 4 } } { 2 x ^ { 7 } }2x78x10+6x9−6x7+6x5+5x4​

13x

Factor the trinomial. - 16x2−56x−3216 x ^ { 2 } - 56 x - 3216x2−56x−32

Subtract. - (5x2+9x−4)−(−10x2−3)\left( 5 x ^ { 2 } + 9 x - 4 \right) - \left( - 10 x ^ { 2 } - 3 \right)(5x2+9x−4)−(−10x2−3)

Factor the polynomial. - 14x6+8x4+16x214 x ^ { 6 } + 8 x ^ { 4 } + 16 x ^ { 2 }14x6+8x4+16x2

Divide. - y3−125y−5\frac { y ^ { 3 } - 125 } { y - 5 }y−5y3−125​

Find the function. -If P(x)=6x−8P ( x ) = 6 x - 8P(x)=6x−8 , find P(−x)P ( - x )P(−x) .

Factor the polynomial completely. - x2y−49y−x2+49x ^ { 2 } y - 49 y - x ^ { 2 } + 49x2y−49y−x2+49

Factor. - 49x3y−42x2y2+9xy349 x ^ { 3 } y - 42 x ^ { 2 } y ^ { 2 } + 9 x y ^ { 3 }49x3y−42x2y2+9xy3