dividing polynomials multiple choice, math homework help

Simplify the expression.

$fraction numerator 9 a cubed b squared minus 18 a squared b cubed over denominator 3 a squared b end fraction$

3 a b space minus space 18 a squared b cubed

3 a b space minus space 6 b squared

3 a to the power of 3 divided by 2 space end exponent b squared minus 6 a b cubed

6 a b space minus space 15 a b cubed_x000D_

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Simplify the expression.

$fraction numerator 5 x y squared minus space 6 y cubed plus 3 x squared y cubed over denominator x y end fraction$

$5 y minus fraction numerator 6 y squared over denominator x end fraction plus 3 x y squared$

5 x y space minus space 3 x y squared

5 y space minus space 6 x y squared plus 3 x squared y squared

$fraction numerator 5 y over denominator x end fraction minus space fraction numerator 6 y squared over denominator x end fraction plus space 3 x y squared$

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Simplify the expression.

$fraction numerator y cubed plus 3 y squared minus 5 y space minus space 4 over denominator y plus 4 end fraction$

y squared minus y space minus 1

y cubed minus y squared minus space y

$y squared plus 7 y space plus space 23 space plus space fraction numerator 88 over denominator y plus 4 end fraction$

$y squared plus space 7 y space minus space 33 space plus space fraction numerator 128 over denominator y plus 4 end fraction$

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left parenthesis t to the power of 5 minus 3 t squared minus space 10 right parenthesis space divided by space left parenthesis t minus 2 right parenthesis

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Which of the following shows the solution when the following synthetic division model is set up?

x to the power of 4 minus 3 x cubed plus 16 x squared minus 48 x space plus space 145

$x cubed minus 3 x squared plus 16 x space minus 48 space plus fraction numerator 145 over denominator x minus 3 end fraction$

$x cubed minus space 3 x squared plus 16 x minus 48 space plus space fraction numerator 145 over denominator x plus 3 end fraction$

x to the power of 4 plus 3 x cubed plus 16 x squared plus 48 x space plus 145

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Simplify the expression

$fraction numerator x cubed minus 3 x squared plus x minus 3 over denominator x to the power of 2 space end exponent plus 1 end fraction$

$x squared minus 4 x plus 5 space minus space fraction numerator 8 over denominator x squared plus 1 end fraction$

x-3

$x squared minus 4 space plus space fraction numerator x plus 1 over denominator x squared plus 1 end fraction$

$x minus 4 space plus space fraction numerator 5 x minus 3 over denominator x squared plus 1 end fraction$

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Simplify the expression

left parenthesis 6 t cubed plus 5 t squared plus 9 right parenthesis divided by left parenthesis 2 t space plus space 3 right parenthesis

3t2 -2t +3

$3 t squared space minus space 2 t space plus fraction numerator 3 over denominator 2 t plus 3 end fraction$

$3 t squared plus fraction numerator 5 t over denominator 2 end fraction plus 3$

$6 t squared minus 13 t space plus 39 space minus space fraction numerator 108 over denominator 2 t plus 3 end fraction$

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Simplify the expression.

$fraction numerator 2 x to the power of 4 plus 3 x cubed minus 2 x squared minus 3 x minus 6 over denominator 2 x plus 3 end fraction$

$x cubed plus 3 x squared plus 3.5 x space plus space 3.75 space plus space fraction numerator 5.25 over denominator 2 x plus 3 end fraction$

$x cubed plus 3 over 2 x squared space minus space x minus space 3 over 2 minus space fraction numerator 6 over denominator 2 x plus 3 end fraction$

$x cubed minus x squared space minus space fraction numerator 6 over denominator 2 x plus 3 end fraction$

$x cubed minus x space minus space fraction numerator 6 over denominator 2 x plus 3 end fraction$

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Simplify the expression.

$fraction numerator 2 x to the power of 4 plus 3 x cubed minus 2 x squared minus 3 x minus 6 over denominator 2 x plus 3 end fraction$

$x cubed plus 3 x squared plus 3.5 x space plus space 3.75 space plus space fraction numerator 5.25 over denominator 2 x plus 3 end fraction$

$x cubed plus 3 over 2 x squared space minus space x minus space 3 over 2 minus space fraction numerator 6 over denominator 2 x plus 3 end fraction$

$x cubed minus x squared space minus space fraction numerator 6 over denominator 2 x plus 3 end fraction$

$x cubed minus x space minus space fraction numerator 6 over denominator 2 x plus 3 end fraction$

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Divide,

left parenthesis 3 x to the power of 5 minus x cubed plus 4 x squared minus space 12 x minus 8 right parenthesis divided by left parenthesis x squared minus 2 right parenthesis

$3 x cubed minus space 7 x plus 4 space minus space fraction numerator 26 x over denominator x squared minus 2 end fraction$

$3 x cubed plus 5 x space plus space 4 space minus space fraction numerator 2 x over denominator x squared minus 2 end fraction$

$3 x cubed plus 5 x cubed plus 14 x space plus space 16 space equals space fraction numerator 24 over denominator x to the power of 2 space end exponent minus 2 end fraction$

$3 x to the power of 4 plus 6 x to the power of 4 plus 11 x cubed plus 26 x space plus space 40 space plus space fraction numerator 72 over denominator x squared minus space 2 end fraction$

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Divide.

left parenthesis 2 x to the power of 5 minus 6 x to the power of 4 plus x cubed minus 4 x plus 3 right parenthesis space divided by space left parenthesis x squared minus space 3 right parenthesis

$2 x cubed minus 6 x squared plus 7 x space minus 18 space plus space fraction numerator 17 x minus 51 over denominator x squared minus 3 end fraction$

$2 x cubed minus 6 x squared plus 7 x space minus space 22 space plus space fraction numerator 21 x minus 63 over denominator x to the power of 2 space end exponent minus 3 end fraction$

$2 x to the power of 4 space end exponent plus x squared minus x minus 3 space minus space fraction numerator 6 over denominator x squared minus 3 end fraction$