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Algebraic division of polynomials.

28 k 3 p 42 kp 2 + 56 kp 3 14 kp size 12{ { {"28"k rSup { size 8{3} } p - "42" ital "kp" rSup { size 8{2} } +"56" ital "kp" rSup { size 8{3} } } over {"14" ital "kp"} } } {} =

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x 2 12 x 45 x + 3 size 12{ { {x rSup { size 8{2} } - "12"x - "45"} over {x+3} } } {} =

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  • A

    2y 2 + y 16 y 3 size 12{ { {2y rSup { size 8{2} } +y - "16"} over {y - 3} } } {} =
  • B

    Test your answer by choosing a number for y and seeing if you get the same answer.
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2h 3 5h 2 + 22 h + 51 2h + 3 size 12{ { {2h rSup { size 8{3} } - 5h rSup { size 8{2} } +"22"h+"51"} over {2h+3} } } {} =

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2x 3 4x 2 + 6x 15 x 2 + 3 size 12{ { {2x rSup { size 8{3} } - 4x rSup { size 8{2} } +6x - "15"} over {x rSup { size 8{2} } +3} } } {} =

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x 3 4x 2 x 4 size 12{ { {x rSup { size 8{3} } - 4x rSup { size 8{2} } } over {x - 4} } } {} =

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  • A

    x 3 27 x 3 size 12{ { {x rSup { size 8{3} } - "27"} over {x - 3} } } {} =
  • B

    Test your answer by multiplying back.
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After dividing two polynomials, I get the answer r 2 6 r + 9 1 r 3 size 12{ { {1} over {r - 3} } } {} . What two polynomials did I divide?

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Source:  OpenStax, Advanced algebra ii: activities and homework. OpenStax CNX. Sep 15, 2009 Download for free at http://cnx.org/content/col10686/1.5
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