Question 1

Determine the coefficient and the degree of each term in the polynomial
-$$9 x ^ { 8 } + 10 x$$

Accepted Answer

A)  Coefficients: 9, 10
 degrees: 9, 1 
B)  Coefficients: $9,10,1$
degrees: $8,1,0$ 
C)  Coefficients: 9,10
degrees: 8, 1 
D)  Coefficients: 9, 10 
degrees: 8,0 
A)  Coefficients: 9, 10
 degrees: 9, 1 
B)  Coefficients: $9,10,1$
degrees: $8,1,0$ 
C)  Coefficients: 9,10
degrees: 8, 1 
D)  Coefficients: 9, 10 
degrees: 8,0

Question 2

Simplify. (Assume all variables are nonzero.)
-$\frac { 20 x ^ { 9 } y ^ { 3 } z ^ { 7 } } { 4 x ^ { 5 } y ^ { 3 } z ^ { 3 } }$

Accepted Answer

A)  $16 x^{4} z^{4}$ 
B)  $5 x^{4} Z^{4}$ 
C)  $5 \mathrm { x } ^ { 14 } \mathrm { z }^{ 10}$ 
D)  $5 x^{45}{z}^{21}$ 
A)  $16 x^{4} z^{4}$ 
B)  $5 x^{4} Z^{4}$ 
C)  $5 \mathrm { x } ^ { 14 } \mathrm { z }^{ 10}$ 
D)  $5 x^{45}{z}^{21}$

Question 3

For the given functions f(x) and g(x), perform the indicated operation.
-$$f ( x ) = x ^ { 3 } - 9 x - 27 , g ( x ) = 3 x ^ { 3 } + x ^ { 2 } + 5 x + 13$$
Find $f ( x ) + g ( x )$.

Accepted Answer

A)  $4 x ^ { 3 } - x ^ { 2 } - 4 x + 14$ 
B)  $3 x ^ { 3 } + x ^ { 2 } - 4 x - 14$ 
C)  $4 x ^ { 3 } + x ^ { 2 } - 14 x - 40$ 
D)  $4 x ^ { 3 } + x ^ { 2 } - 4 x - 14$ 
A)  $4 x ^ { 3 } - x ^ { 2 } - 4 x + 14$ 
B)  $3 x ^ { 3 } + x ^ { 2 } - 4 x - 14$ 
C)  $4 x ^ { 3 } + x ^ { 2 } - 14 x - 40$ 
D)  $4 x ^ { 3 } + x ^ { 2 } - 4 x - 14$

Question 4

Add or subtract.
-$\left( - 5 m n + 3 m n ^ { 2 } - 3 m ^ { 2 } n ^ { 2 } \right) + \left( 5 m ^ { 2 } n + 6 m ^ { 2 } n ^ { 2 } - 6 m n \right)$

Accepted Answer

A)  $- 11 m n + 8 m ^ { 2 } n + 3 m ^ { 2 } n ^ { 2 }$ 
B)  $1 m n + 3 m n ^ { 2 } + 5 m ^ { 2 } n + 3 m ^ { 2 } n ^ { 2 }$ 
C)  $3 m ^ { 2 } n ^ { 2 } + 5 m ^ { 2 } n + 3 m n ^ { 2 } - 11 m n$ 
D)  $0 m ^ { 2 } n ^ { 2 }$ 
A)  $- 11 m n + 8 m ^ { 2 } n + 3 m ^ { 2 } n ^ { 2 }$ 
B)  $1 m n + 3 m n ^ { 2 } + 5 m ^ { 2 } n + 3 m ^ { 2 } n ^ { 2 }$ 
C)  $3 m ^ { 2 } n ^ { 2 } + 5 m ^ { 2 } n + 3 m n ^ { 2 } - 11 m n$ 
D)  $0 m ^ { 2 } n ^ { 2 }$

Question 5

Simplify. (Assume all variables are nonzero.)
-$\frac { a ^ { 9 } b ^ { 7 } } { a ^ { 3 } b }$

Accepted Answer

A)  $( a b ) ^ { 19 }$ 
B)  $a ^ { 6 } b ^ { 6 }$ 
C)  $a ^ { 27 } b ^ { 7 }$ 
D)  21 
A)  $( a b ) ^ { 19 }$ 
B)  $a ^ { 6 } b ^ { 6 }$ 
C)  $a ^ { 27 } b ^ { 7 }$ 
D)  21

Question 6

Add or subtract.
-$$\left( 5 x ^ { 8 } - 8 x ^ { 3 } + 7 x ^ { 2 } + 6 \right) + \left( 4 x ^ { 7 } + 5 x ^ { 3 } - 9 x \right)$$

Accepted Answer

A)  $9 x ^ { 8 } - 13 x ^ { 3 } + 7 x ^ { 2 } - 9 x + 6$ 
B)  $5 x ^ { 8 } + 4 x ^ { 7 } - 3 x ^ { 3 } + 7 x ^ { 2 } - 9 x + 6$ 
C)  $5 x ^ { 8 } + 4 x ^ { 7 } + 3 x ^ { 3 } + 7 x ^ { 2 } - 9 x + 6$ 
D)  $9 x ^ { 8 } - 3 x ^ { 3 } + 7 x ^ { 2 } - 9 x + 6$ 
A)  $9 x ^ { 8 } - 13 x ^ { 3 } + 7 x ^ { 2 } - 9 x + 6$ 
B)  $5 x ^ { 8 } + 4 x ^ { 7 } - 3 x ^ { 3 } + 7 x ^ { 2 } - 9 x + 6$ 
C)  $5 x ^ { 8 } + 4 x ^ { 7 } + 3 x ^ { 3 } + 7 x ^ { 2 } - 9 x + 6$ 
D)  $9 x ^ { 8 } - 3 x ^ { 3 } + 7 x ^ { 2 } - 9 x + 6$

Question 7

Multiply.
-$$- 10 x ^ { 2 } y ^ { 6 } \left( - 11 x ^ { 6 } y ^ { 6 } + 6 y ^ { 5 } - 6 x \right)$$

Accepted Answer

A)  $110 x ^ { 6 } y ^ { 6 } - 60 y ^ { 5 } + 60 x$ 
B)  $110 x ^ { 8 } y ^ { 12 } - 60 x ^ { 3 } y ^ { 11 } - 6 x$ 
C)  $110 x ^ { 8 } y ^ { 12 } + 6 y ^ { 5 } - 6 x$ 
D)  $110 x ^ { 8 } y ^ { 12 } - 60 x ^ { 2 } y ^ { 11 } + 60 x ^ { 3 } y ^ { 6 }$ 
A)  $110 x ^ { 6 } y ^ { 6 } - 60 y ^ { 5 } + 60 x$ 
B)  $110 x ^ { 8 } y ^ { 12 } - 60 x ^ { 3 } y ^ { 11 } - 6 x$ 
C)  $110 x ^ { 8 } y ^ { 12 } + 6 y ^ { 5 } - 6 x$ 
D)  $110 x ^ { 8 } y ^ { 12 } - 60 x ^ { 2 } y ^ { 11 } + 60 x ^ { 3 } y ^ { 6 }$

Question 8

Find the missing monomial, factor or term.
-(?) $) ^ { 2 } = x ^ { 2 } + 24 x + 144$

Accepted Answer

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

Question 9

Find the missing factor or exponent(s).
-$$\left( x ^ { 10 } \right) ^ { ? } = x ^ { 20 }$$

Accepted Answer

A)  20 
B)  10 
C)  2 
D)  18 
A)  20 
B)  10 
C)  2 
D)  18

Question 10

Find the missing factor or exponent(s).
-$$\left( \frac { x ^ { 15 } y ^ { 10 } } { z ^ { 8 } } \right) ^ { ? } = \frac { x ^ { 135 } y ^ { 90 } } { z ^ { 72 } }$$

Accepted Answer

A)  8 
B)  10 
C)  15 
D)  9 
A)  8 
B)  10 
C)  15 
D)  9

Question 11

Multiply.
-$$- 4 x ^ { 2 } \left( x ^ { 2 } - 3 x - 11 \right)$$

Accepted Answer

A)  $- 4 x ^ { 4 } + 12 x ^ { 3 } + 44 x ^ { 2 }$ 
B)  $- 4 x ^ { 4 } - 12 x ^ { 3 } + 44 x ^ { 2 }$ 
C)  $4 x ^ { 4 } + 12 x ^ { 3 } - 44 x ^ { 2 }$ 
D)  $4 x ^ { 4 } - 12 x ^ { 3 } - 44 x ^ { 2 }$ 
A)  $- 4 x ^ { 4 } + 12 x ^ { 3 } + 44 x ^ { 2 }$ 
B)  $- 4 x ^ { 4 } - 12 x ^ { 3 } + 44 x ^ { 2 }$ 
C)  $4 x ^ { 4 } + 12 x ^ { 3 } - 44 x ^ { 2 }$ 
D)  $4 x ^ { 4 } - 12 x ^ { 3 } - 44 x ^ { 2 }$

Question 12

Identify the polynomial as a monomial, binomial or trinomial.
-$$16 x ^ { 5 } + 6 x ^ { 4 } - 8 x ^ { 3 }$$

Accepted Answer

A)  Binomial 
B)  Trinomial 
C)  Monomial 
A)  Binomial 
B)  Trinomial 
C)  Monomial

Question 13

Multiply.
-$10 x ^ { 9 } \cdot 5 x ^ { 6 }$

Accepted Answer

A)  $50 x ^{15}$ 
B)  $50 x^{ 54}$ 
C)  $100 x^{ 15}$ 
D)  $15 x^{ 15}$ 
A)  $50 x ^{15}$ 
B)  $50 x^{ 54}$ 
C)  $100 x^{ 15}$ 
D)  $15 x^{ 15}$

Question 14

Find the missing monomial, factor or term.
-$$? \left( - 5 z ^ { 2 } - 3 z - 1 \right) = - 35 z ^ { 3 } - 21 z ^ { 2 } - 7 z$$

Accepted Answer

A)  $- 35 z$ 
B)  $7 \mathrm { z } ^ { 3 }$ 
C)  $7 \mathrm { z }$ 
D)  $7 \mathrm { z } ^ { 2 }$ 
A)  $- 35 z$ 
B)  $7 \mathrm { z } ^ { 3 }$ 
C)  $7 \mathrm { z }$ 
D)  $7 \mathrm { z } ^ { 2 }$

Question 15

Rewrite the polynomial in descending order. Identify the leading term, the leading coefficient, and the degree of the
polynomial.
-$$- 4 x ^ { 2 } + 3 x ^ { 3 } + 6 x ^ { 4 } + 3$$

Accepted Answer

A)  $- 4 x ^ { 2 } , 4,2$ 
B)  $3 x ^ { 3 } , 3,3$ 
C)  $6 x ^ { 4 } , 6,4$ 
D)  $- 4 x ^ { 2 } , - 4,2$ 
A)  $- 4 x ^ { 2 } , 4,2$ 
B)  $3 x ^ { 3 } , 3,3$ 
C)  $6 x ^ { 4 } , 6,4$ 
D)  $- 4 x ^ { 2 } , - 4,2$

Question 16

Simplify. (Assume all variables are nonzero.)
-$( - 8 ) ^ { 0 }$

Accepted Answer

A)  $- 8$ 
B)  0 
C)  $- 1$ 
D)  1 
A)  $- 8$ 
B)  0 
C)  $- 1$ 
D)  1

Question 17

Simplify.
-$\left( x ^ { 6 } \right) ^ { 3 }$

Accepted Answer

A)  $x ^ { 12 }$ 
B)  $x ^ { 11 }$ 
C)  $x ^ { 18 }$ 
D)  $x ^ { 9 }$ 
A)  $x ^ { 12 }$ 
B)  $x ^ { 11 }$ 
C)  $x ^ { 18 }$ 
D)  $x ^ { 9 }$

Question 18

Evaluate the polynomial or polynomial function for the given value of the variable.
-$- 4 x ^ { 2 } + 9 x + 5$ for $x = 2$

Accepted Answer

A)  $- 3$ 
B)  7 
C)  3 
D)  15 
A)  $- 3$ 
B)  7 
C)  3 
D)  15

Question 19

-$$\left( 7 x ^ { 6 } y ^ { 5 } z ^ { 5 } \right) ^ { 0 }$$

Accepted Answer

A)  1 
B)  0 
C)  $7 x ^ { 6 } y ^ { 5 } z ^ { 5 }$ 
D)  7 
A)  1 
B)  0 
C)  $7 x ^ { 6 } y ^ { 5 } z ^ { 5 }$ 
D)  7

Question 20

Find the missing factor or exponent(s).
-$$\frac { x ^ { 14 } y ^ { ? } } { x ^ { ? } y ^ { 20 } } = x ^ { 7 } y ^ { 12 }$$

Accepted Answer

A)  14,7 
B)  20,14 
C)  7,32 
D)  7,20 
A)  14,7 
B)  20,14 
C)  7,32 
D)  7,20

Determine the coefficient and the degree of each term in the polynomial - $9 x ^ { 8 } + 10 x$

Simplify. (Assume all variables are nonzero.) - $\frac { 20 x ^ { 9 } y ^ { 3 } z ^ { 7 } } { 4 x ^ { 5 } y ^ { 3 } z ^ { 3 } }$

For the given functions f(x) and g(x), perform the indicated operation. - $f ( x ) = x ^ { 3 } - 9 x - 27 , g ( x ) = 3 x ^ { 3 } + x ^ { 2 } + 5 x + 13$ Find $f ( x ) + g ( x )$ .

Add or subtract. - $\left( - 5 m n + 3 m n ^ { 2 } - 3 m ^ { 2 } n ^ { 2 } \right) + \left( 5 m ^ { 2 } n + 6 m ^ { 2 } n ^ { 2 } - 6 m n \right)$

Simplify. (Assume all variables are nonzero.) - $\frac { a ^ { 9 } b ^ { 7 } } { a ^ { 3 } b }$

Add or subtract. - $\left( 5 x ^ { 8 } - 8 x ^ { 3 } + 7 x ^ { 2 } + 6 \right) + \left( 4 x ^ { 7 } + 5 x ^ { 3 } - 9 x \right)$

Multiply. - $- 10 x ^ { 2 } y ^ { 6 } \left( - 11 x ^ { 6 } y ^ { 6 } + 6 y ^ { 5 } - 6 x \right)$

Find the missing monomial, factor or term. -(?) $) ^ { 2 } = x ^ { 2 } + 24 x + 144$

Find the missing factor or exponent(s). - $\left( x ^ { 10 } \right) ^ { ? } = x ^ { 20 }$

Find the missing factor or exponent(s). - $\left( \frac { x ^ { 15 } y ^ { 10 } } { z ^ { 8 } } \right) ^ { ? } = \frac { x ^ { 135 } y ^ { 90 } } { z ^ { 72 } }$

Multiply. - $- 4 x ^ { 2 } \left( x ^ { 2 } - 3 x - 11 \right)$

Identify the polynomial as a monomial, binomial or trinomial. - $16 x ^ { 5 } + 6 x ^ { 4 } - 8 x ^ { 3 }$

Multiply. - $10 x ^ { 9 } \cdot 5 x ^ { 6 }$

Find the missing monomial, factor or term. - $? \left( - 5 z ^ { 2 } - 3 z - 1 \right) = - 35 z ^ { 3 } - 21 z ^ { 2 } - 7 z$

Rewrite the polynomial in descending order. Identify the leading term, the leading coefficient, and the degree of the polynomial. - $- 4 x ^ { 2 } + 3 x ^ { 3 } + 6 x ^ { 4 } + 3$

Simplify. (Assume all variables are nonzero.) - $( - 8 ) ^ { 0 }$

Simplify. - $\left( x ^ { 6 } \right) ^ { 3 }$

Evaluate the polynomial or polynomial function for the given value of the variable. - $- 4 x ^ { 2 } + 9 x + 5$ for $x = 2$

$- \left( 7 x ^ { 6 } y ^ { 5 } z ^ { 5 } \right) ^ { 0 }$ $- \left( 7 x ^ { 6 } y ^ { 5 } z ^ { 5 } \right) ^ { 0 }$ - $\left( 7 x ^ { 6 } y ^ { 5 } z ^ { 5 } \right) ^ { 0 }$

Find the missing factor or exponent(s). - $\frac { x ^ { 14 } y ^ { ? } } { x ^ { ? } y ^ { 20 } } = x ^ { 7 } y ^ { 12 }$

Review of Real Numbers

Linear Equations

Graphing Linear Equations

Systems of Equations

Factoring and Quadratic Equations

Rational Expressions and Equations

A Transition

Radical Expressions and Equations

Quadratic Equations

Functions

Logarithmic and Exponential Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 5: Exponents and Polynomials

Determine the coefficient and the degree of each term in the polynomial - 9x8+10x9 x ^ { 8 } + 10 x9x8+10x

Simplify. (Assume all variables are nonzero.) - 20x9y3z74x5y3z3\frac { 20 x ^ { 9 } y ^ { 3 } z ^ { 7 } } { 4 x ^ { 5 } y ^ { 3 } z ^ { 3 } }4x5y3z320x9y3z7​

For the given functions f(x) and g(x), perform the indicated operation. - f(x)=x3−9x−27,g(x)=3x3+x2+5x+13f ( x ) = x ^ { 3 } - 9 x - 27 , g ( x ) = 3 x ^ { 3 } + x ^ { 2 } + 5 x + 13f(x)=x3−9x−27,g(x)=3x3+x2+5x+13 Find f(x)+g(x)f ( x ) + g ( x )f(x)+g(x) .

Add or subtract. - (−5mn+3mn2−3m2n2)+(5m2n+6m2n2−6mn)\left( - 5 m n + 3 m n ^ { 2 } - 3 m ^ { 2 } n ^ { 2 } \right) + \left( 5 m ^ { 2 } n + 6 m ^ { 2 } n ^ { 2 } - 6 m n \right)(−5mn+3mn2−3m2n2)+(5m2n+6m2n2−6mn)

Simplify. (Assume all variables are nonzero.) - a9b7a3b\frac { a ^ { 9 } b ^ { 7 } } { a ^ { 3 } b }a3ba9b7​

Add or subtract. - (5x8−8x3+7x2+6)+(4x7+5x3−9x)\left( 5 x ^ { 8 } - 8 x ^ { 3 } + 7 x ^ { 2 } + 6 \right) + \left( 4 x ^ { 7 } + 5 x ^ { 3 } - 9 x \right)(5x8−8x3+7x2+6)+(4x7+5x3−9x)

Multiply. - −10x2y6(−11x6y6+6y5−6x)- 10 x ^ { 2 } y ^ { 6 } \left( - 11 x ^ { 6 } y ^ { 6 } + 6 y ^ { 5 } - 6 x \right)−10x2y6(−11x6y6+6y5−6x)

Find the missing monomial, factor or term. -(?) )2=x2+24x+144) ^ { 2 } = x ^ { 2 } + 24 x + 144)2=x2+24x+144

Find the missing factor or exponent(s). - (x10)?=x20\left( x ^ { 10 } \right) ^ { ? } = x ^ { 20 }(x10)?=x20

Find the missing factor or exponent(s). - (x15y10z8)?=x135y90z72\left( \frac { x ^ { 15 } y ^ { 10 } } { z ^ { 8 } } \right) ^ { ? } = \frac { x ^ { 135 } y ^ { 90 } } { z ^ { 72 } }(z8x15y10​)?=z72x135y90​

Multiply. - −4x2(x2−3x−11)- 4 x ^ { 2 } \left( x ^ { 2 } - 3 x - 11 \right)−4x2(x2−3x−11)

Identify the polynomial as a monomial, binomial or trinomial. - 16x5+6x4−8x316 x ^ { 5 } + 6 x ^ { 4 } - 8 x ^ { 3 }16x5+6x4−8x3

Multiply. - 10x9⋅5x610 x ^ { 9 } \cdot 5 x ^ { 6 }10x9⋅5x6

Find the missing monomial, factor or term. - ?(−5z2−3z−1)=−35z3−21z2−7z? \left( - 5 z ^ { 2 } - 3 z - 1 \right) = - 35 z ^ { 3 } - 21 z ^ { 2 } - 7 z?(−5z2−3z−1)=−35z3−21z2−7z

Rewrite the polynomial in descending order. Identify the leading term, the leading coefficient, and the degree of the polynomial. - −4x2+3x3+6x4+3- 4 x ^ { 2 } + 3 x ^ { 3 } + 6 x ^ { 4 } + 3−4x2+3x3+6x4+3

Simplify. (Assume all variables are nonzero.) - (−8)0( - 8 ) ^ { 0 }(−8)0

Simplify. - (x6)3\left( x ^ { 6 } \right) ^ { 3 }(x6)3

Evaluate the polynomial or polynomial function for the given value of the variable. - −4x2+9x+5- 4 x ^ { 2 } + 9 x + 5−4x2+9x+5 for x=2x = 2x=2

- (7x6y5z5)0\left( 7 x ^ { 6 } y ^ { 5 } z ^ { 5 } \right) ^ { 0 }(7x6y5z5)0

Find the missing factor or exponent(s). - x14y?x?y20=x7y12\frac { x ^ { 14 } y ^ { ? } } { x ^ { ? } y ^ { 20 } } = x ^ { 7 } y ^ { 12 }x?y20x14y?​=x7y12