Question 1

For the given functions f(x) and g(x), find f(x) ∙ g(x).
-$$f ( x ) = 8 x ^ { 3 } , g ( x ) = 6 x ^ { 4 }$$

Accepted Answer

A)  $48 x ^ { 7 }$ 
B)  $14 x ^ { 7 }$ 
C)  $48 x ^ { 12 }$ 
D)  $14 x ^ { 12 }$ 
A)  $48 x ^ { 7 }$ 
B)  $14 x ^ { 7 }$ 
C)  $48 x ^ { 12 }$ 
D)  $14 x ^ { 12 }$

Question 2

Solve the problem. Express your answer in scientific notation, and round to one decimal place.
-The sun radiates energy into space at the rate of $3.9 \times 10 ^ { 26 }$ joules per second. How many joules are emitted in two weeks?

Accepted Answer

A)  $4.7 \times 10 ^ { 26 }$ joules 
B)  $4.7 \times 10 ^ { 50 }$ joules 
C)  $4.7 \times 10 ^ { 32 }$ joules 
D)  $4.7 \times 1044$ joules 
A)  $4.7 \times 10 ^ { 26 }$ joules 
B)  $4.7 \times 10 ^ { 50 }$ joules 
C)  $4.7 \times 10 ^ { 32 }$ joules 
D)  $4.7 \times 1044$ joules

Question 3

Evaluate the polynomial.
-$- x y z + x ^ { 5 } + z ^ { 4 }$ for $x = 1 , y = - 1$ and $z = 2$

Accepted Answer

A)  35 
B)  15 
C)  19 
D)  21 
A)  35 
B)  15 
C)  19 
D)  21

Question 4

Evaluate the polynomial or polynomial function for the given value of the variable.
-$$f ( x ) = - 5 x ^ { 3 } + 4 x ^ { 2 } - 45 , f ( - 2 )$$

Accepted Answer

A)  11 
B)  1 
C)  $- 13$ 
D)  $- 1$ 
A)  11 
B)  1 
C)  $- 13$ 
D)  $- 1$

Question 5

Divide using long division.
-$$\frac { 2 x ^ { 2 } + 11 x - 40 } { 2 x - 5 }$$

Accepted Answer

A)  $x + 8$ 
B)  $x - 11$ 
C)  $x + 8 + \frac { 2 } { 2 x - 5 }$ 
D)  $x - 8 + \frac { 3 } { 2 x - 5 }$ 
A)  $x + 8$ 
B)  $x - 11$ 
C)  $x + 8 + \frac { 2 } { 2 x - 5 }$ 
D)  $x - 8 + \frac { 3 } { 2 x - 5 }$

Question 6

Divide using long division.
-$$\left( x ^ { 2 } + 2 x - 8 \right) \div ( x + 4 )$$

Accepted Answer

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

Question 7

For the given functions f(x) and g(x), find f(x) ∙ g(x).
-$$f ( x ) = x ^ { 3 } - 4 x ^ { 2 } + 2 x + 7 , g ( x ) = - 5 x ^ { 3 }$$

Accepted Answer

A)  $- 5 x ^ { 9 } + 20 x ^ { 6 } - 10 x ^ { 4 } - 35 x ^ { 3 }$ 
B)  $- 5 x ^ { 9 } - 20 x ^ { 6 } + 10 x ^ { 4 } + 35 x ^ { 3 }$ 
C)  $- 5 x ^ { 6 } - 20 x ^ { 5 } + 10 x ^ { 4 } + 35 x ^ { 3 }$ 
D)  $- 5 x ^ { 6 } + 20 x ^ { 5 } - 10 x ^ { 4 } - 35 x ^ { 3 }$ 
A)  $- 5 x ^ { 9 } + 20 x ^ { 6 } - 10 x ^ { 4 } - 35 x ^ { 3 }$ 
B)  $- 5 x ^ { 9 } - 20 x ^ { 6 } + 10 x ^ { 4 } + 35 x ^ { 3 }$ 
C)  $- 5 x ^ { 6 } - 20 x ^ { 5 } + 10 x ^ { 4 } + 35 x ^ { 3 }$ 
D)  $- 5 x ^ { 6 } + 20 x ^ { 5 } - 10 x ^ { 4 } - 35 x ^ { 3 }$

Question 8

Simplify.
-$\left( 5 x ^ { 3 } \right) ^ { 3 }$

Accepted Answer

A)  $5 x ^ { 9 }$ 
B)  $15 x ^ { 9 }$ 
C)  $15 x ^ { 6 }$ 
D)  $125 \mathrm { x } ^ { 9 }$ 
A)  $5 x ^ { 9 }$ 
B)  $15 x ^ { 9 }$ 
C)  $15 x ^ { 6 }$ 
D)  $125 \mathrm { x } ^ { 9 }$

Question 9

Divide using long division.
-$$\frac { - 6 x ^ { 3 } - 4 x ^ { 2 } + 13 x + 13 } { - 3 x + 4 }$$

Accepted Answer

A)  $2 x ^ { 2 } + 4 x + 1$ 
B)  $x ^ { 2 } + 1 + \frac { 4 } { - 3 x + 4 }$ 
C)  $2 x ^ { 2 } + 4 x + 1 + \frac { 9 } { - 3 x + 4 }$ 
D)  $2 x ^ { 2 } + 4 x + 1 + \frac { 12 } { - 3 x + 4 }$ 
A)  $2 x ^ { 2 } + 4 x + 1$ 
B)  $x ^ { 2 } + 1 + \frac { 4 } { - 3 x + 4 }$ 
C)  $2 x ^ { 2 } + 4 x + 1 + \frac { 9 } { - 3 x + 4 }$ 
D)  $2 x ^ { 2 } + 4 x + 1 + \frac { 12 } { - 3 x + 4 }$

Question 10

Multiply.
-$$( 5 y - 9 ) \left( 25 y ^ { 2 } + 45 y + 81 \right)$$

Accepted Answer

A)  $25 y ^ { 3 } + 729$ 
B)  $125 \mathrm { y } ^ { 3 } - 729$ 
C)  $125 y ^ { 3 } + 405 y ^ { 2 } - 729$ 
D)  $125 \mathrm { y } ^ { 3 } + 729$ 
A)  $25 y ^ { 3 } + 729$ 
B)  $125 \mathrm { y } ^ { 3 } - 729$ 
C)  $125 y ^ { 3 } + 405 y ^ { 2 } - 729$ 
D)  $125 \mathrm { y } ^ { 3 } + 729$

Question 11

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero
real numbers.)
-$\frac { y ^ { - 15 } } { y ^ { 2 } }$

Accepted Answer

A)  $\mathrm { y } ^ { 13 }$ 
B)  $\frac { 1 } { y ^ { 13 } }$ 
C)  $\frac { 1 } { y ^ { 17 } }$ 
D)  $\mathrm { y } ^ { 17 }$ 
A)  $\mathrm { y } ^ { 13 }$ 
B)  $\frac { 1 } { y ^ { 13 } }$ 
C)  $\frac { 1 } { y ^ { 17 } }$ 
D)  $\mathrm { y } ^ { 17 }$

Question 12

-$\left( \frac { x ^ { 3 } } { y ^ { 3 } z ^ { 5 } } \right) ^ { 2 }$

Accepted Answer

A)  $\frac { x ^ { 5 } } { y ^ { 6 } z ^ { 7 } }$ 
B)  $\frac { x ^ { 6 } } { y ^ { 6 } z }$ 
C)  $\frac { x ^ { 6 } } { y ^ { 3 } z ^ { 10 } }$ 
D)  $\frac { x ^ { 6 } } { y ^ { 5 } z ^ { 10 } }$ 
A)  $\frac { x ^ { 5 } } { y ^ { 6 } z ^ { 7 } }$ 
B)  $\frac { x ^ { 6 } } { y ^ { 6 } z }$ 
C)  $\frac { x ^ { 6 } } { y ^ { 3 } z ^ { 10 } }$ 
D)  $\frac { x ^ { 6 } } { y ^ { 5 } z ^ { 10 } }$

Question 13

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

Accepted Answer

A)  $2 x ^ { 2 } y - 8 x - 2 y ^ { 2 }$ 
B)  $2 x ^ { 2 } y - 16 x - 2 y ^ { 2 }$ 
C)  $2 x ^ { 4 } y - 16 x ^ { 2 } - 2 y ^ { 2 }$ 
D)  $- 35 x ^ { 2 } y - 8 x - 2 y ^ { 2 }$ 
A)  $2 x ^ { 2 } y - 8 x - 2 y ^ { 2 }$ 
B)  $2 x ^ { 2 } y - 16 x - 2 y ^ { 2 }$ 
C)  $2 x ^ { 4 } y - 16 x ^ { 2 } - 2 y ^ { 2 }$ 
D)  $- 35 x ^ { 2 } y - 8 x - 2 y ^ { 2 }$

Question 14

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

Accepted Answer

A)  $- 4 x ^ { 2 } y z ^ { 2 } + 11 x y ^ { 2 } - 6 x y z$ 
B)  $- 4 x ^ { 2 } y z ^ { 2 } - 11 x y ^ { 2 } + 2 x y z$ 
C)  $- 4 x ^ { 2 } y z ^ { 2 } - 11 x y ^ { 2 } - 6 x y z$ 
D)  $2 x ^ { 2 } y z ^ { 2 } + 5 x y ^ { 2 } - 6 x y z$ 
A)  $- 4 x ^ { 2 } y z ^ { 2 } + 11 x y ^ { 2 } - 6 x y z$ 
B)  $- 4 x ^ { 2 } y z ^ { 2 } - 11 x y ^ { 2 } + 2 x y z$ 
C)  $- 4 x ^ { 2 } y z ^ { 2 } - 11 x y ^ { 2 } - 6 x y z$ 
D)  $2 x ^ { 2 } y z ^ { 2 } + 5 x y ^ { 2 } - 6 x y z$

Question 15

Determine the coefficient and the degree of each term in the polynomial
-$$- 4 x ^ { 4 } - 14 x ^ { 2 } + 7 x + 5 x ^ { 6 }$$

Accepted Answer

A)  Coefficients: $- 4 , - 14 , - 7 , - 5$
degrees: $4,2,1,6$ 
B)  Coefficients: $4,2,1,6$ 
degrees: $- 4 , - 14,7,5$ 
C)  Coefficients: $- 4 , - 14,7,5$
degrees: $4,2,0,6$ 
D)  Coefficients: $- 4 , - 14,7,5$ 
degrees: $4,2,1,6$ 
A)  Coefficients: $- 4 , - 14 , - 7 , - 5$
degrees: $4,2,1,6$ 
B)  Coefficients: $4,2,1,6$ 
degrees: $- 4 , - 14,7,5$ 
C)  Coefficients: $- 4 , - 14,7,5$
degrees: $4,2,0,6$ 
D)  Coefficients: $- 4 , - 14,7,5$ 
degrees: $4,2,1,6$

Question 16

Add or subtract.
-$$\left( 4 x ^ { 2 } + 7 x - 5 \right) + \left( 5 x ^ { 2 } - 10 x + 13 \right)$$

Accepted Answer

A)  $9 x ^ { 2 } - 3 x + 8$ 
B)  $9 x ^ { 2 } - 17 x + 8$ 
C)  $9 x ^ { 2 } + 3 x + 8$ 
D)  $9 x ^ { 2 } - 3 x + 18$ 
A)  $9 x ^ { 2 } - 3 x + 8$ 
B)  $9 x ^ { 2 } - 17 x + 8$ 
C)  $9 x ^ { 2 } + 3 x + 8$ 
D)  $9 x ^ { 2 } - 3 x + 18$

Question 17

Divide. Assume all variables are nonzero.
-$$\left( 12 x ^ { 6 } \right) \div \left( 3 x ^ { 2 } \right)$$

Accepted Answer

A)  16 
B)  $9 x ^ { 4 }$ 
C)  $4 x ^ { 8 }$ 
D)  $4 x ^ { 4 }$ 
A)  16 
B)  $9 x ^ { 4 }$ 
C)  $4 x ^ { 8 }$ 
D)  $4 x ^ { 4 }$

Question 18

Find the special product using the appropriate formula.
-$$( x + 15 ) ^ { 2 }$$

Accepted Answer

A)  $x ^ { 2 } + 30 x + 225$ 
B)  $x + 225$ 
C)  $225 x ^ { 2 } + 30 x + 225$ 
D)  $x ^ { 2 } + 225$ 
A)  $x ^ { 2 } + 30 x + 225$ 
B)  $x + 225$ 
C)  $225 x ^ { 2 } + 30 x + 225$ 
D)  $x ^ { 2 } + 225$

Question 19

Multiply.
-$- 7 x ^ { 3 } \cdot 8 x ^ { 3 }$

Accepted Answer

A)  $- 56 x ^ { 9 }$ 
B)  $15 x ^ { 9 }$ 
C)  $- 56 x ^ { 6 }$ 
D)  $15 x ^ { 6 }$ 
A)  $- 56 x ^ { 9 }$ 
B)  $15 x ^ { 9 }$ 
C)  $- 56 x ^ { 6 }$ 
D)  $15 x ^ { 6 }$

Question 20

Multiply.
-$$- 9 x ^ { 5 } \cdot 7 x ^ { 7 } \cdot 2 x ^ { 5 }$$

Accepted Answer

A)  $126 x ^ { 175 }$ 
B)  $126 x^{ 17}$ 
C)  $- 126 x ^ { 175 }$ 
D)  $- 126 \mathrm { x } ^ { 17 }$ 
A)  $126 x ^ { 175 }$ 
B)  $126 x^{ 17}$ 
C)  $- 126 x ^ { 175 }$ 
D)  $- 126 \mathrm { x } ^ { 17 }$

For the given functions f(x) and g(x), find f(x) ∙ g(x). - $f ( x ) = 8 x ^ { 3 } , g ( x ) = 6 x ^ { 4 }$

Solve the problem. Express your answer in scientific notation, and round to one decimal place. -The sun radiates energy into space at the rate of $3.9 \times 10 ^ { 26 }$ joules per second. How many joules are emitted in two weeks?

Evaluate the polynomial. - $- x y z + x ^ { 5 } + z ^ { 4 }$ for $x = 1 , y = - 1$ and $z = 2$

Evaluate the polynomial or polynomial function for the given value of the variable. - $f ( x ) = - 5 x ^ { 3 } + 4 x ^ { 2 } - 45 , f ( - 2 )$

Divide using long division. - $\frac { 2 x ^ { 2 } + 11 x - 40 } { 2 x - 5 }$

Divide using long division. - $\left( x ^ { 2 } + 2 x - 8 \right) \div ( x + 4 )$

For the given functions f(x) and g(x), find f(x) ∙ g(x). - $f ( x ) = x ^ { 3 } - 4 x ^ { 2 } + 2 x + 7 , g ( x ) = - 5 x ^ { 3 }$

Simplify. - $\left( 5 x ^ { 3 } \right) ^ { 3 }$

Divide using long division. - $\frac { - 6 x ^ { 3 } - 4 x ^ { 2 } + 13 x + 13 } { - 3 x + 4 }$

Multiply. - $( 5 y - 9 ) \left( 25 y ^ { 2 } + 45 y + 81 \right)$

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.) - $\frac { y ^ { - 15 } } { y ^ { 2 } }$

$- \left( \frac { x ^ { 3 } } { y ^ { 3 } z ^ { 5 } } \right) ^ { 2 }$ $- \left( \frac { x ^ { 3 } } { y ^ { 3 } z ^ { 5 } } \right) ^ { 2 }$ - $\left( \frac { x ^ { 3 } } { y ^ { 3 } z ^ { 5 } } \right) ^ { 2 }$

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

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

Determine the coefficient and the degree of each term in the polynomial - $- 4 x ^ { 4 } - 14 x ^ { 2 } + 7 x + 5 x ^ { 6 }$

Add or subtract. - $\left( 4 x ^ { 2 } + 7 x - 5 \right) + \left( 5 x ^ { 2 } - 10 x + 13 \right)$

Divide. Assume all variables are nonzero. - $\left( 12 x ^ { 6 } \right) \div \left( 3 x ^ { 2 } \right)$

Find the special product using the appropriate formula. - $( x + 15 ) ^ { 2 }$

Multiply. - $- 7 x ^ { 3 } \cdot 8 x ^ { 3 }$

Multiply. - $- 9 x ^ { 5 } \cdot 7 x ^ { 7 } \cdot 2 x ^ { 5 }$

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

For the given functions f(x) and g(x), find f(x) ∙ g(x). - f(x)=8x3,g(x)=6x4f ( x ) = 8 x ^ { 3 } , g ( x ) = 6 x ^ { 4 }f(x)=8x3,g(x)=6x4

Solve the problem. Express your answer in scientific notation, and round to one decimal place. -The sun radiates energy into space at the rate of 3.9×10263.9 \times 10 ^ { 26 }3.9×1026 joules per second. How many joules are emitted in two weeks?

Evaluate the polynomial. - −xyz+x5+z4- x y z + x ^ { 5 } + z ^ { 4 }−xyz+x5+z4 for x=1,y=−1x = 1 , y = - 1x=1,y=−1 and z=2z = 2z=2

Evaluate the polynomial or polynomial function for the given value of the variable. - f(x)=−5x3+4x2−45,f(−2)f ( x ) = - 5 x ^ { 3 } + 4 x ^ { 2 } - 45 , f ( - 2 )f(x)=−5x3+4x2−45,f(−2)

Divide using long division. - 2x2+11x−402x−5\frac { 2 x ^ { 2 } + 11 x - 40 } { 2 x - 5 }2x−52x2+11x−40​

Divide using long division. - (x2+2x−8)÷(x+4)\left( x ^ { 2 } + 2 x - 8 \right) \div ( x + 4 )(x2+2x−8)÷(x+4)

For the given functions f(x) and g(x), find f(x) ∙ g(x). - f(x)=x3−4x2+2x+7,g(x)=−5x3f ( x ) = x ^ { 3 } - 4 x ^ { 2 } + 2 x + 7 , g ( x ) = - 5 x ^ { 3 }f(x)=x3−4x2+2x+7,g(x)=−5x3

Simplify. - (5x3)3\left( 5 x ^ { 3 } \right) ^ { 3 }(5x3)3

Divide using long division. - −6x3−4x2+13x+13−3x+4\frac { - 6 x ^ { 3 } - 4 x ^ { 2 } + 13 x + 13 } { - 3 x + 4 }−3x+4−6x3−4x2+13x+13​

Multiply. - (5y−9)(25y2+45y+81)( 5 y - 9 ) \left( 25 y ^ { 2 } + 45 y + 81 \right)(5y−9)(25y2+45y+81)

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.) - y−15y2\frac { y ^ { - 15 } } { y ^ { 2 } }y2y−15​

- (x3y3z5)2\left( \frac { x ^ { 3 } } { y ^ { 3 } z ^ { 5 } } \right) ^ { 2 }(y3z5x3​)2

Add or subtract. - (−5x2y−8x+3y2)+(7x2y−8x−5y2)\left( - 5 x ^ { 2 } y - 8 x + 3 y ^ { 2 } \right) + \left( 7 x ^ { 2 } y - 8 x - 5 y ^ { 2 } \right)(−5x2y−8x+3y2)+(7x2y−8x−5y2)

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

Determine the coefficient and the degree of each term in the polynomial - −4x4−14x2+7x+5x6- 4 x ^ { 4 } - 14 x ^ { 2 } + 7 x + 5 x ^ { 6 }−4x4−14x2+7x+5x6

Add or subtract. - (4x2+7x−5)+(5x2−10x+13)\left( 4 x ^ { 2 } + 7 x - 5 \right) + \left( 5 x ^ { 2 } - 10 x + 13 \right)(4x2+7x−5)+(5x2−10x+13)

Divide. Assume all variables are nonzero. - (12x6)÷(3x2)\left( 12 x ^ { 6 } \right) \div \left( 3 x ^ { 2 } \right)(12x6)÷(3x2)

Find the special product using the appropriate formula. - (x+15)2( x + 15 ) ^ { 2 }(x+15)2

Multiply. - −7x3⋅8x3- 7 x ^ { 3 } \cdot 8 x ^ { 3 }−7x3⋅8x3

Multiply. - −9x5⋅7x7⋅2x5- 9 x ^ { 5 } \cdot 7 x ^ { 7 } \cdot 2 x ^ { 5 }−9x5⋅7x7⋅2x5