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Subtract the polynomials. Assume all variable exponents represent whole numbers. -Subtract 9x3+11x2y+8xy2+10y39 x ^ { 3 } + 11 x ^ { 2 } y + 8 x y ^ { 2 } + 10 y ^ { 3 } from 2x3+3xy2+12y32 x ^ { 3 } + 3 x y ^ { 2 } + 12 y ^ { 3 }


A) 7x3+11x2y+5xy2−2y37 x ^ { 3 } + 11 x ^ { 2 } y + 5 x y ^ { 2 } - 2 y ^ { 3 }
B) −7x3−11x2y−5xy2+2y3- 7 x ^ { 3 } - 11 x ^ { 2 } y - 5 x y ^ { 2 } + 2 y ^ { 3 }
C) 11x3+11x2y+10xy2+22y311 x ^ { 3 } + 11 x ^ { 2 } y + 10 x y ^ { 2 } + 22 y ^ { 3 }
D) −7x3+11x2y−5xy2+2y3- 7 x ^ { 3 } + 11 x ^ { 2 } y - 5 x y ^ { 2 } + 2 y ^ { 3 }

Correct Answer

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Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end behavior to match the function with its graph. - f(x) =6x3−3x2−3x−2f ( x ) = 6 x ^ { 3 } - 3 x ^ { 2 } - 3 x - 2


A) rises to the left and rises to the right
Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end behavior to match the function with its graph. - f ( x ) = 6 x ^ { 3 } - 3 x ^ { 2 } - 3 x - 2 A) rises to the left and rises to the right B) falls to the left and falls to the right C) rises to the left and falls to the right D) falls to the left and rises to the right
B) falls to the left and falls to the right
Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end behavior to match the function with its graph. - f ( x ) = 6 x ^ { 3 } - 3 x ^ { 2 } - 3 x - 2 A) rises to the left and rises to the right B) falls to the left and falls to the right C) rises to the left and falls to the right D) falls to the left and rises to the right
C) rises to the left and falls to the right
Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end behavior to match the function with its graph. - f ( x ) = 6 x ^ { 3 } - 3 x ^ { 2 } - 3 x - 2 A) rises to the left and rises to the right B) falls to the left and falls to the right C) rises to the left and falls to the right D) falls to the left and rises to the right
D) falls to the left and rises to the right
Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end behavior to match the function with its graph. - f ( x ) = 6 x ^ { 3 } - 3 x ^ { 2 } - 3 x - 2 A) rises to the left and rises to the right B) falls to the left and falls to the right C) rises to the left and falls to the right D) falls to the left and rises to the right

Correct Answer

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Solve the problem. -A rocket is stopped 28 feet from a satellite when it begins accelerating away from the satellite at a constant rate of 10 feet per second per second. The distance between the rocket and the satellite is given by the polynomial P(t) =5t2+28\mathrm { P } ( \mathrm { t } ) = 5 \mathrm { t } ^ { 2 } + 28 . Find the distance between the rocket and the satellite 9 seconds after the rocket started moving.


A) 109ft109 \mathrm { ft }
B) 73ft73 \mathrm { ft }
C) 405ft405 \mathrm { ft }
D) 433ft433 \mathrm { ft }

Correct Answer

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Add the polynomials. Assume all variable exponents represent whole numbers. - (3y2n+5yn+4) +(5y2n+5yn+8) \left( 3 y ^ { 2 n } + 5 y ^ { n } + 4 \right) + \left( 5 y ^ { 2 n } + 5 y ^ { n } + 8 \right)


A) 8y4n+10y2n+128 y ^ { 4 n } + 10 y ^ { 2 n } + 12
B) 9y2n+8yn+139 y ^ { 2 n } + 8 y ^ { n } + 13
C) 30y3n30 y ^ { 3 n }
D) 8y2n+10yn+128 y ^ { 2 n } + 10 y ^ { n } + 12

Correct Answer

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Multiply using the rule for the product of the sum and difference of two terms. Assume any variable exponents represent whole numbers. - (1+x3) (1−x3) \left( 1 + x ^ { 3 } \right) \left( 1 - x ^ { 3 } \right)


A) 2−x62 - x ^ { 6 }
B) 2−x92 - x ^ { 9 }
C) 1−x61 - x ^ { 6 }
D) 1−x91 - x ^ { 9 }

Correct Answer

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Find the indicated function value. -Find f(2) f ( 2 ) when f(x) =x3+4x2+9xf ( x ) = x ^ { 3 } + 4 x ^ { 2 } + 9 x .


A) −6- 6
B) 26
C) 6
D) 42

Correct Answer

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Multiply using one of the rules for the square of a binomial. Assume any variable exponents represent whole numbers. - (5x+y) 2( 5 x + y ) ^ { 2 }


A) 25x2+10xy+y225 x ^ { 2 } + 10 x y + y ^ { 2 }
B) 25x2+5xy+y225 x ^ { 2 } + 5 x y + y ^ { 2 }
C) 25x2+10xy+2y225 x ^ { 2 } + 10 x y + 2 y ^ { 2 }
D) 5x2+10xy+y25 x ^ { 2 } + 10 x y + y ^ { 2 }

Correct Answer

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Factor the greatest common factor from the polynomial. Assume any variable exponents represent whole numbers. - y2+4yy ^ { 2 } + 4 y


A) y2(1+4y) y ^ { 2 } ( 1 + 4 y )
B) y(y+4) y ( y + 4 )
C) 4y(y+1) 4 y ( y + 1 )
D) 4(y2+y) 4 \left( y ^ { 2 } + y \right)

Correct Answer

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Find the product. Assume all variable exponents represent whole numbers. - (p−q) (p2+pq+q2) ( p - q ) \left( p ^ { 2 } + p q + q ^ { 2 } \right)


A) p3−q3p ^ { 3 } - q ^ { 3 }
B) p3−2p2q−2pq2−q3p ^ { 3 } - 2 p ^ { 2 } q - 2 p q ^ { 2 } - q ^ { 3 }
C) p3+2p2q+2pq2−q3p ^ { 3 } + 2 p ^ { 2 } q + 2 p q ^ { 2 } - q ^ { 3 }
D) p3+q3\mathrm { p } ^ { 3 } + \mathrm { q } ^ { 3 }

Correct Answer

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Multiply using the rule for the product of the sum and difference of two terms. Assume any variable exponents represent whole numbers. - (x−3) (x+3) (x2+9) ( x - 3 ) ( x + 3 ) \left( x ^ { 2 } + 9 \right)


A) x4+18x2+81x ^ { 4 } + 18 x ^ { 2 } + 81
B) x4−81x ^ { 4 } - 81
C) x4+6x3+18x2−54x−81x ^ { 4 } + 6 x ^ { 3 } + 18 x ^ { 2 } - 54 x - 81
D) x4+6x3−54x−81x ^ { 4 } + 6 x ^ { 3 } - 54 x - 81

Correct Answer

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Solve the problem. -Write a polynomial that represents the volume of the open box. Solve the problem. -Write a polynomial that represents the volume of the open box. A) 45 x + 154 x ^ { 2 } + 121 x ^ { 3 } B) 45 x - 154 x ^ { 2 } + 11 x ^ { 3 } C) 45 - 154 x + 121 x ^ { 2 } D) 45 x - 154 x ^ { 2 } + 121 x ^ { 3 }


A) 45x+154x2+121x345 x + 154 x ^ { 2 } + 121 x ^ { 3 }
B) 45x−154x2+11x345 x - 154 x ^ { 2 } + 11 x ^ { 3 }
C) 45−154x+121x245 - 154 x + 121 x ^ { 2 }
D) 45x−154x2+121x345 x - 154 x ^ { 2 } + 121 x ^ { 3 }

Correct Answer

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Multiply using the rule for the product of the sum and difference of two terms. Assume any variable exponents represent whole numbers. - (8an−13bn) (8an+13bn) \left( 8 a ^ { n } - 13 b ^ { n } \right) \left( 8 a ^ { n } + 13 b ^ { n } \right)


A) 8a2n−13b2n8 a ^ { 2 n } - 13 b ^ { 2 n }
B) 64a2n+208anbn−169b2n64 a ^ { 2 n } + 208 a ^ { n } b ^ { n } - 169 b ^ { 2 n }
C) 64an−169bn64 a ^ { n } - 169 b ^ { n }
D) 64a2n−169 b2n64 \mathrm { a } ^ { 2 \mathrm { n } } - 169 \mathrm {~b} ^ { 2 \mathrm { n } }

Correct Answer

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Solve the problem. -Write a polynomial that represents the area of the shaded region. Solve the problem. -Write a polynomial that represents the area of the shaded region. A) 67 x ^ { 2 } - 9 B) 61 x ^ { 2 } + 9 C) 64 x ^ { 2 } - 3 x - 9 D) 61 \mathrm { x } ^ { 2 } - 9


A) 67x2−967 x ^ { 2 } - 9
B) 61x2+961 x ^ { 2 } + 9
C) 64x2−3x−964 x ^ { 2 } - 3 x - 9
D) 61x2−961 \mathrm { x } ^ { 2 } - 9

Correct Answer

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Multiply using the rule for the product of the sum and difference of two terms. Assume any variable exponents represent whole numbers. - (2x+11y) (2x−11y) ( 2 x + 11 y ) ( 2 x - 11 y )


A) 2x2−11y22 x ^ { 2 } - 11 y ^ { 2 }
B) 4x2+44xy−121y24 x ^ { 2 } + 44 x y - 121 y ^ { 2 }
C) 4x2−44xy−121y24 x ^ { 2 } - 44 x y - 121 y ^ { 2 }
D) 4x2−121y24 x ^ { 2 } - 121 y ^ { 2 }

Correct Answer

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Multiply the monomial and the polynomial. Assume any variable exponents represent whole numbers. - 12ab2(9a2b3+10ab) 12 a b ^ { 2 } \left( 9 a ^ { 2 } b ^ { 3 } + 10 a b \right)


A) 108a3b5+120a2b3108 a ^ { 3 } b ^ { 5 } + 120 a ^ { 2 } b ^ { 3 }
B) 108a3b4+120a2b3108 a ^ { 3 } b ^ { 4 } + 120 a ^ { 2 } b ^ { 3 }
C) 108a2b5+120a2b3108 a ^ { 2 } b ^ { 5 } + 120 a ^ { 2 } b ^ { 3 }
D) 108a3b5+120a2b2108 a ^ { 3 } b ^ { 5 } + 120 a ^ { 2 } b ^ { 2 }

Correct Answer

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Find the product. Assume all variable exponents represent whole numbers. - (x−11) (x2+2x−8) ( x - 11 ) \left( x ^ { 2 } + 2 x - 8 \right)


A) x3−9x2−30x+88x ^ { 3 } - 9 x ^ { 2 } - 30 x + 88
B) x3+13x2+30x+88x ^ { 3 } + 13 x ^ { 2 } + 30 x + 88
C) x3+13x2+14x−88x ^ { 3 } + 13 x ^ { 2 } + 14 x - 88
D) x3−9x2−14x−88x ^ { 3 } - 9 x ^ { 2 } - 14 x - 88

Correct Answer

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Use the FOIL method to multiply the binomials. Assume any variable exponents represent whole numbers. - (3xy+5) (4xy+9) ( 3 x y + 5 ) ( 4 x y + 9 )


A) 12x2y2+47xy+1412 x ^ { 2 } y ^ { 2 } + 47 x y + 14
B) 12x2y2+27xy+4512 x ^ { 2 } y ^ { 2 } + 27 x y + 45
C) 12x2y2+47xy+4512 x ^ { 2 } y ^ { 2 } + 47 x y + 45
D) 7x2y2+47xy+457 x ^ { 2 } y ^ { 2 } + 47 x y + 45

Correct Answer

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Factor the greatest common factor from the polynomial. Assume any variable exponents represent whole numbers. - 36x5y+28xy436 x ^ { 5 } y + 28 x y ^ { 4 }


A) 4y(9x5+7xy3) 4 y \left( 9 x ^ { 5 } + 7 x y ^ { 3 } \right)
B) 4x(9x4y+7y4) 4 x \left( 9 x ^ { 4 } y + 7 y ^ { 4 } \right)
C) xy(36x4+28y3) x y \left( 36 x ^ { 4 } + 28 y ^ { 3 } \right)
D) 4xy(9x4+7y3) 4 x y \left( 9 x ^ { 4 } + 7 y ^ { 3 } \right)

Correct Answer

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Multiply using one of the rules for the square of a binomial. Assume any variable exponents represent whole numbers. - (3x−7y) 2( 3 x - 7 y ) ^ { 2 }


A) 9x2−42xy+49y29 x ^ { 2 } - 42 x y + 49 y ^ { 2 }
B) 3x2+49y23 x ^ { 2 } + 49 y ^ { 2 }
C) 3x2−42xy+49y23 x ^ { 2 } - 42 x y + 49 y ^ { 2 }
D) 9x2+49y29 x ^ { 2 } + 49 y ^ { 2 }

Correct Answer

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Find the indicated function value. -Find f(4) f ( 4 ) when f(x) =x2−5x−7f ( x ) = x ^ { 2 } - 5 x - 7


A) 3
B) 43
C) −11- 11
D) 29

Correct Answer

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