Question 1

Use substitution to factor the polynomial completely.
-$8 x ^ { 4 } - 6 x ^ { 2 } - 9$

Accepted Answer

A)  $\left( 2 x ^ { 2 } - 3 \right) \left( 4 x ^ { 2 } + 3 \right)$ 
B)  $\left( 2 x ^ { 2 } + 1 \right) \left( 4 x ^ { 2 } - 9 \right)$ 
C)  $( 4 x - 3 ) ( 2 x + 3 )$ 
D)  $\left( 8 x ^ { 2 } - 3 \right) \left( x ^ { 2 } + 3 \right)$ 
A)  $\left( 2 x ^ { 2 } - 3 \right) \left( 4 x ^ { 2 } + 3 \right)$ 
B)  $\left( 2 x ^ { 2 } + 1 \right) \left( 4 x ^ { 2 } - 9 \right)$ 
C)  $( 4 x - 3 ) ( 2 x + 3 )$ 
D)  $\left( 8 x ^ { 2 } - 3 \right) \left( x ^ { 2 } + 3 \right)$

Question 2

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

Accepted Answer

A)  $( 8 x + 8 ) ( y + 1 )$ 
B)  $( x + 8 ) ( y + 1 )$ 
C)  $( x + 1 ) ( y + 8 )$ 
D)  $( x + 1 ) ( 8 y + 8 )$ 
A)  $( 8 x + 8 ) ( y + 1 )$ 
B)  $( x + 8 ) ( y + 1 )$ 
C)  $( x + 1 ) ( y + 8 )$ 
D)  $( x + 1 ) ( 8 y + 8 )$

Question 3

Simplify the polynomial by combining like terms.
-$$- 9 x y + 8 y ^ { 2 } - 2 x y + 8 x ^ { 2 }$$

Accepted Answer

A)  $- 11 x y + 64 x ^ { 2 } y ^ { 2 }$ 
B)  $18 x y + 64 x ^ { 2 } y ^ { 2 }$ 
C)  $8 x ^ { 2 } - 11 x y + 8 y ^ { 2 }$ 
D)  $5 x ^ { 2 } + 5 x y + 5 y ^ { 2 }$ 
A)  $- 11 x y + 64 x ^ { 2 } y ^ { 2 }$ 
B)  $18 x y + 64 x ^ { 2 } y ^ { 2 }$ 
C)  $8 x ^ { 2 } - 11 x y + 8 y ^ { 2 }$ 
D)  $5 x ^ { 2 } + 5 x y + 5 y ^ { 2 }$

Question 4

Simplify the polynomial by combining like terms.
-$$\begin{array} { r } 
3 x ^ { 5 } + 5 x ^ { 2 } + 5 \
+ \left( 6 x ^ { 5 } - 9 x ^ { 2 } - 7 \right) \
\hline
\end{array}$$

Accepted Answer

A)  $11 x ^ { 5 } - 6 x ^ { 2 } - 2$ 
B)  $9 - 4 x ^ { 5 } - 2 x ^ { 2 }$ 
C)  $3 x ^ { 7 }$ 
D)  $9 x ^ { 5 } - 4 x ^ { 2 } - 2$ 
A)  $11 x ^ { 5 } - 6 x ^ { 2 } - 2$ 
B)  $9 - 4 x ^ { 5 } - 2 x ^ { 2 }$ 
C)  $3 x ^ { 7 }$ 
D)  $9 x ^ { 5 } - 4 x ^ { 2 } - 2$

Question 5

Factor.
-$$x ^ { 3 } y ^ { 2 } + 512 y ^ { 2 }$$

Accepted Answer

A)  $y ^ { 2 } ( x - 8 ) \left( x ^ { 2 } + 8 x + 64 \right)$ 
B)  $y ^ { 2 } ( x + 8 ) \left( x ^ { 2 } + 64 \right)$ 
C)  $y ^ { 2 } ( x + 8 ) \left( x ^ { 2 } - 8 x + 64 \right)$ 
D)  $( x y + 8 ) \left( x ^ { 2 } y ^ { 2 } - 8 x + 64 \right)$ 
A)  $y ^ { 2 } ( x - 8 ) \left( x ^ { 2 } + 8 x + 64 \right)$ 
B)  $y ^ { 2 } ( x + 8 ) \left( x ^ { 2 } + 64 \right)$ 
C)  $y ^ { 2 } ( x + 8 ) \left( x ^ { 2 } - 8 x + 64 \right)$ 
D)  $( x y + 8 ) \left( x ^ { 2 } y ^ { 2 } - 8 x + 64 \right)$

Question 6

Factor.
-$729 x ^ { 3 } - 343$

Accepted Answer

A)  $( 9 x - 7 ) \left( 81 x ^ { 2 } + 63 x + 49 \right)$ 
B)  $( 9 x + 7 ) \left( 81 x ^ { 2 } - 63 x + 49 \right)$ 
C)  $( 9 x - 7 ) \left( 81 x ^ { 2 } + 49 \right)$ 
D)  $( 729 x - 7 ) \left( x ^ { 2 } + 63 x + 49 \right)$ 
A)  $( 9 x - 7 ) \left( 81 x ^ { 2 } + 63 x + 49 \right)$ 
B)  $( 9 x + 7 ) \left( 81 x ^ { 2 } - 63 x + 49 \right)$ 
C)  $( 9 x - 7 ) \left( 81 x ^ { 2 } + 49 \right)$ 
D)  $( 729 x - 7 ) \left( x ^ { 2 } + 63 x + 49 \right)$

Question 7

Find the GCF of the list of monomials.
-$12 x ^ { 2 } y , 20 x ^ { 2 } y ^ { 2 } , 24 x ^ { 3 } y ^ { 2 }$

Accepted Answer

A)  $12 x y$ 
B)  $x ^ { 2 } y ^ { 2 }$ 
C)  $8 x ^ { 3 } y ^ { 2 }$ 
D)  $4 x ^ { 2 } y$ 
A)  $12 x y$ 
B)  $x ^ { 2 } y ^ { 2 }$ 
C)  $8 x ^ { 3 } y ^ { 2 }$ 
D)  $4 x ^ { 2 } y$

Question 8

Factor the polynomial completely.
-$$x ^ { 2 } - 6 x y - 16 y ^ { 2 }$$

Accepted Answer

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

Question 9

Simplify the polynomial by combining like terms.
-$$- 11 x ^ { 9 } - 8 x ^ { 3 } y - 3 x ^ { 9 } - \frac { 1 } { 9 } - 1 x ^ { 3 } y - 4 x ^ { 9 }$$

Accepted Answer

A)  $- 18 x ^ { 9 } - 9 x ^ { 3 } y - \frac { 1 } { 9 }$ 
B)  $- 27 x ^ { 9 } - \frac { 1 } { 9 }$ 
C)  $- 18 x ^ { 9 } - 8 x ^ { 3 } y - \frac { 1 } { 9 }$ 
D)  $- 27 x ^ { 9 } - 27 x ^ { 3 } y - \frac { 1 } { 9 }$ 
A)  $- 18 x ^ { 9 } - 9 x ^ { 3 } y - \frac { 1 } { 9 }$ 
B)  $- 27 x ^ { 9 } - \frac { 1 } { 9 }$ 
C)  $- 18 x ^ { 9 } - 8 x ^ { 3 } y - \frac { 1 } { 9 }$ 
D)  $- 27 x ^ { 9 } - 27 x ^ { 3 } y - \frac { 1 } { 9 }$

Question 10

Solve.
-If the cost, $C ( x )$, for manufacturing $x$ units of a certain product is given by $C ( x ) = x ^ { 2 } - 30 x + 10,800$, find the number of units manufactured at a cost of $\$ 13,600$.

Accepted Answer

A)  90 units 
B)  120 units 
C)  40 units 
D)  70 units 
A)  90 units 
B)  120 units 
C)  40 units 
D)  70 units

Question 11

Subtract.
-Subtract $\left( 3.5 x ^ { 2 } - x - 9.4 \right)$ from the sum of $\left( 1.7 x ^ { 3 } + 7.8 x ^ { 2 } + 4.7 \right)$ and $( 6.9 x - 2.8 )$.

Accepted Answer

A)  $1.7 x ^ { 3 } + 4.3 x ^ { 2 } + 6.9 x + 11.3$ 
B)  $13.9 x ^ { 6 } + 11.3$ 
C)  $1.7 x ^ { 3 } + 4.3 x ^ { 2 } + 7.9 x + 11.3$ 
D)  $1.7 x ^ { 3 } + 11.3 x ^ { 2 } + 5.9 x - 7.5$ 
A)  $1.7 x ^ { 3 } + 4.3 x ^ { 2 } + 6.9 x + 11.3$ 
B)  $13.9 x ^ { 6 } + 11.3$ 
C)  $1.7 x ^ { 3 } + 4.3 x ^ { 2 } + 7.9 x + 11.3$ 
D)  $1.7 x ^ { 3 } + 11.3 x ^ { 2 } + 5.9 x - 7.5$

Question 12

Subtract.
-$$\left( 3 x ^ { 9 } - 2 x ^ { 8 } + 9 x ^ { 7 } + 4 \right) - \left( 8 x ^ { 9 } + 4 x ^ { 8 } + 5 x ^ { 7 } + 8 \right)$$

Accepted Answer

A)  $- 5 x ^ { 9 } - 6 x ^ { 8 } + 4 x ^ { 7 } - 4$ 
B)  $- 5 x ^ { 9 } + 2 x ^ { 8 } + 14 x ^ { 7 } + 12$ 
C)  $11 x ^ { 9 } + 2 x ^ { 8 } + 14 x ^ { 7 } + 12$ 
D)  $11 x ^ { 9 } + 2 x ^ { 8 } + 14 x ^ { 7 } - 4$ 
A)  $- 5 x ^ { 9 } - 6 x ^ { 8 } + 4 x ^ { 7 } - 4$ 
B)  $- 5 x ^ { 9 } + 2 x ^ { 8 } + 14 x ^ { 7 } + 12$ 
C)  $11 x ^ { 9 } + 2 x ^ { 8 } + 14 x ^ { 7 } + 12$ 
D)  $11 x ^ { 9 } + 2 x ^ { 8 } + 14 x ^ { 7 } - 4$

Question 13

Factor.
-$$x ^ { 2 } - 9 x + 81$$

Accepted Answer

A)  $( x + 9 ) ^ { 2 }$ 
B)  $( x + 9 ) ( x - 9 )$ 
C)  $( x - 9 ) ^ { 2 }$ 
D)  prime polynomial 
A)  $( x + 9 ) ^ { 2 }$ 
B)  $( x + 9 ) ( x - 9 )$ 
C)  $( x - 9 ) ^ { 2 }$ 
D)  prime polynomial

Question 14

Factor completely.
-$$\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 16 }$$

Accepted Answer

A)  $\left( \frac { x } { 5 } - \frac { y } { 4 } \right) ^ { 2 }$ 
B)  $\left( \frac { x } { 5 } + \frac { y } { 4 } \right) ^ { 2 }$ 
C)  $\left( \frac { x } { 5 } + \frac { y } { 4 } \right) \left( \frac { x } { 5 } - \frac { y } { 4 } \right)$ 
D)  prime poplynomial 
A)  $\left( \frac { x } { 5 } - \frac { y } { 4 } \right) ^ { 2 }$ 
B)  $\left( \frac { x } { 5 } + \frac { y } { 4 } \right) ^ { 2 }$ 
C)  $\left( \frac { x } { 5 } + \frac { y } { 4 } \right) \left( \frac { x } { 5 } - \frac { y } { 4 } \right)$ 
D)  prime poplynomial

Question 15

Factor. Assume that variables used as exponents represent positive integers.
-$$x ^ { 4 n } - 1$$

Accepted Answer

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

Question 16

Factor the polynomial.
-$16 x ^ { 9 } y ^ { 8 } - 48 x ^ { 5 } y ^ { 6 } + 24 x ^ { 3 } y ^ { 4 }$

Accepted Answer

A)  $8 \left( 2 x ^ { 9 } y ^ { 8 } - 6 x ^ { 5 } y ^ { 6 } + 3 x ^ { 3 } y ^ { 4 } \right)$ 
B)  $8 x ^ { 3 } y ^ { 4 } \left( 2 x ^ { 6 } y ^ { 4 } - 6 x ^ { 2 } y ^ { 2 } + 3 \right)$ 
C)  $x ^ { 3 } y ^ { 4 } \left( 16 x ^ { 6 } y ^ { 4 } - 48 x ^ { 2 } y ^ { 2 } + 24 \right)$ 
D)  $8 x ^ { 3 } \left( 2 x ^ { 6 } y ^ { 8 } - 6 x ^ { 2 } y ^ { 6 } + 3 y ^ { 4 } \right)$ 
A)  $8 \left( 2 x ^ { 9 } y ^ { 8 } - 6 x ^ { 5 } y ^ { 6 } + 3 x ^ { 3 } y ^ { 4 } \right)$ 
B)  $8 x ^ { 3 } y ^ { 4 } \left( 2 x ^ { 6 } y ^ { 4 } - 6 x ^ { 2 } y ^ { 2 } + 3 \right)$ 
C)  $x ^ { 3 } y ^ { 4 } \left( 16 x ^ { 6 } y ^ { 4 } - 48 x ^ { 2 } y ^ { 2 } + 24 \right)$ 
D)  $8 x ^ { 3 } \left( 2 x ^ { 6 } y ^ { 8 } - 6 x ^ { 2 } y ^ { 6 } + 3 y ^ { 4 } \right)$

Question 17

Divide.
-$$\left( 35 x ^ { 3 } + x ^ { 2 } - 70 x - 2 \right) \div \left( 5 x ^ { 2 } - 10 \right)$$

Accepted Answer

A)  $7 x + \frac { 2 } { 5 x ^ { 2 } - 10 }$ 
B)  $7 x - \frac { 2 } { 5 x ^ { 2 } - 10 }$ 
C)  $7 x + \frac { 1 } { 5 }$ 
D)  $7 x + 5$ 
A)  $7 x + \frac { 2 } { 5 x ^ { 2 } - 10 }$ 
B)  $7 x - \frac { 2 } { 5 x ^ { 2 } - 10 }$ 
C)  $7 x + \frac { 1 } { 5 }$ 
D)  $7 x + 5$

Question 18

Perform the indicated operations and simplify.
-$$\begin{array} { r } 
5 x ^ { 5 } - 9 x ^ { 4 } + 2 x ^ { 3 } + 3 \
+ \left( 4 x ^ { 5 } - 9 x ^ { 4 } - 8 x ^ { 3 } + 6 \right) \
\hline
\end{array}$$

Accepted Answer

A)  $9 x ^ { 5 } - 18 x ^ { 4 } - 6 x ^ { 3 } + 9$ 
B)  $- 15 x ^ { 24 } + 9$ 
C)  $- 6 x ^ { 5 } - 6 x ^ { 4 } + 11 x ^ { 3 } - 5$ 
D)  $9 x ^ { 10 } - 18 x ^ { 8 } - 6 x ^ { 6 } + 9$ 
A)  $9 x ^ { 5 } - 18 x ^ { 4 } - 6 x ^ { 3 } + 9$ 
B)  $- 15 x ^ { 24 } + 9$ 
C)  $- 6 x ^ { 5 } - 6 x ^ { 4 } + 11 x ^ { 3 } - 5$ 
D)  $9 x ^ { 10 } - 18 x ^ { 8 } - 6 x ^ { 6 } + 9$

Question 19

Find the degree of the polynomial and indicate whether the polynomial is a monomial, binomial, trinomial, or none of
these.
-$$6 x ^ { 4 } - 8 x ^ { 4 } y - 5$$

Accepted Answer

A)  degree 4 ; none of these 
B)  trinomial of degree 4 
C)  trinomial of degree 5 
D)  trinomial of degree 9 
A)  degree 4 ; none of these 
B)  trinomial of degree 4 
C)  trinomial of degree 5 
D)  trinomial of degree 9

Question 20

Multiply.
-$$( - 4 x + 9 ) ( x + 12 )$$

Accepted Answer

A)  $- 4 x ^ { 2 } - 41 x + 108$ 
B)  $- 4 x ^ { 2 } + 108 x - 39$ 
C)  $- 4 x ^ { 2 } - 39 x + 108$ 
D)  $- 4 x ^ { 2 } - 39 x - 39$ 
A)  $- 4 x ^ { 2 } - 41 x + 108$ 
B)  $- 4 x ^ { 2 } + 108 x - 39$ 
C)  $- 4 x ^ { 2 } - 39 x + 108$ 
D)  $- 4 x ^ { 2 } - 39 x - 39$

Use substitution to factor the polynomial completely. - $8 x ^ { 4 } - 6 x ^ { 2 } - 9$

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

Simplify the polynomial by combining like terms. - $- 9 x y + 8 y ^ { 2 } - 2 x y + 8 x ^ { 2 }$

Simplify the polynomial by combining like terms. - 3+5+5 + 6-9-7

Factor. - $x ^ { 3 } y ^ { 2 } + 512 y ^ { 2 }$

Factor. - $729 x ^ { 3 } - 343$

Find the GCF of the list of monomials. - $12 x ^ { 2 } y , 20 x ^ { 2 } y ^ { 2 } , 24 x ^ { 3 } y ^ { 2 }$

Factor the polynomial completely. - $x ^ { 2 } - 6 x y - 16 y ^ { 2 }$

Simplify the polynomial by combining like terms. - $- 11 x ^ { 9 } - 8 x ^ { 3 } y - 3 x ^ { 9 } - \frac { 1 } { 9 } - 1 x ^ { 3 } y - 4 x ^ { 9 }$

Solve. -If the cost, $C ( x )$ , for manufacturing $x$ units of a certain product is given by $C ( x ) = x ^ { 2 } - 30 x + 10,800$ , find the number of units manufactured at a cost of $\$ 13,600$ .

Subtract. -Subtract $\left( 3.5 x ^ { 2 } - x - 9.4 \right)$ from the sum of $\left( 1.7 x ^ { 3 } + 7.8 x ^ { 2 } + 4.7 \right)$ and $( 6.9 x - 2.8 )$ .

Subtract. - $\left( 3 x ^ { 9 } - 2 x ^ { 8 } + 9 x ^ { 7 } + 4 \right) - \left( 8 x ^ { 9 } + 4 x ^ { 8 } + 5 x ^ { 7 } + 8 \right)$

Factor. - $x ^ { 2 } - 9 x + 81$

Factor completely. - $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 16 }$

Factor. Assume that variables used as exponents represent positive integers. - $x ^ { 4 n } - 1$

Factor the polynomial. - $16 x ^ { 9 } y ^ { 8 } - 48 x ^ { 5 } y ^ { 6 } + 24 x ^ { 3 } y ^ { 4 }$

Divide. - $\left( 35 x ^ { 3 } + x ^ { 2 } - 70 x - 2 \right) \div \left( 5 x ^ { 2 } - 10 \right)$

Perform the indicated operations and simplify. - 5-9+2+3 + 4-9-8+6

Find the degree of the polynomial and indicate whether the polynomial is a monomial, binomial, trinomial, or none of these. - $6 x ^ { 4 } - 8 x ^ { 4 } y - 5$

Multiply. - $( - 4 x + 9 ) ( x + 12 )$

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Exam 5: Polynomials and Polynomial Functions

Use substitution to factor the polynomial completely. - 8x4−6x2−98 x ^ { 4 } - 6 x ^ { 2 } - 98x4−6x2−9

Factor the polynomial by grouping. - xy+y+8x+8x y + y + 8 x + 8xy+y+8x+8

Simplify the polynomial by combining like terms. - −9xy+8y2−2xy+8x2- 9 x y + 8 y ^ { 2 } - 2 x y + 8 x ^ { 2 }−9xy+8y2−2xy+8x2

Simplify the polynomial by combining like terms. - 3+5+5 + 6-9-7

Factor. - x3y2+512y2x ^ { 3 } y ^ { 2 } + 512 y ^ { 2 }x3y2+512y2

Factor. - 729x3−343729 x ^ { 3 } - 343729x3−343

Find the GCF of the list of monomials. - 12x2y,20x2y2,24x3y212 x ^ { 2 } y , 20 x ^ { 2 } y ^ { 2 } , 24 x ^ { 3 } y ^ { 2 }12x2y,20x2y2,24x3y2

Factor the polynomial completely. - x2−6xy−16y2x ^ { 2 } - 6 x y - 16 y ^ { 2 }x2−6xy−16y2

Simplify the polynomial by combining like terms. - −11x9−8x3y−3x9−19−1x3y−4x9- 11 x ^ { 9 } - 8 x ^ { 3 } y - 3 x ^ { 9 } - \frac { 1 } { 9 } - 1 x ^ { 3 } y - 4 x ^ { 9 }−11x9−8x3y−3x9−91​−1x3y−4x9

Solve. -If the cost, C(x)C ( x )C(x) , for manufacturing xxx units of a certain product is given by C(x)=x2−30x+10,800C ( x ) = x ^ { 2 } - 30 x + 10,800C(x)=x2−30x+10,800 , find the number of units manufactured at a cost of $13,600\$ 13,600$13,600 .

Subtract. -Subtract (3.5x2−x−9.4)\left( 3.5 x ^ { 2 } - x - 9.4 \right)(3.5x2−x−9.4) from the sum of (1.7x3+7.8x2+4.7)\left( 1.7 x ^ { 3 } + 7.8 x ^ { 2 } + 4.7 \right)(1.7x3+7.8x2+4.7) and (6.9x−2.8)( 6.9 x - 2.8 )(6.9x−2.8) .

Subtract. - (3x9−2x8+9x7+4)−(8x9+4x8+5x7+8)\left( 3 x ^ { 9 } - 2 x ^ { 8 } + 9 x ^ { 7 } + 4 \right) - \left( 8 x ^ { 9 } + 4 x ^ { 8 } + 5 x ^ { 7 } + 8 \right)(3x9−2x8+9x7+4)−(8x9+4x8+5x7+8)

Factor. - x2−9x+81x ^ { 2 } - 9 x + 81x2−9x+81

Factor completely. - x225−y216\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 16 }25x2​−16y2​

Factor. Assume that variables used as exponents represent positive integers. - x4n−1x ^ { 4 n } - 1x4n−1

Factor the polynomial. - 16x9y8−48x5y6+24x3y416 x ^ { 9 } y ^ { 8 } - 48 x ^ { 5 } y ^ { 6 } + 24 x ^ { 3 } y ^ { 4 }16x9y8−48x5y6+24x3y4

Divide. - (35x3+x2−70x−2)÷(5x2−10)\left( 35 x ^ { 3 } + x ^ { 2 } - 70 x - 2 \right) \div \left( 5 x ^ { 2 } - 10 \right)(35x3+x2−70x−2)÷(5x2−10)