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x^4 + 2x^3 - 4x^2 - 8x + ax^2 + 4ax + 4a

 May 2, 2019

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 #1
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\(x^4+2x^3-4x^2-8x+ax^2+4ax+4a\\ =x^3(x+2)-4x(x+2)+a(x+2)^2\\ =(x^3-4x)(x+2)+a(x+2)^2\\ =x(x+2)^2(x-2)+a(x+2)^2\\ =(x+2)^2(x^2-2x+a)\)

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 May 2, 2019
edited by MaxWong  May 2, 2019
 #1
avatar+7763 
+1
Best Answer

\(x^4+2x^3-4x^2-8x+ax^2+4ax+4a\\ =x^3(x+2)-4x(x+2)+a(x+2)^2\\ =(x^3-4x)(x+2)+a(x+2)^2\\ =x(x+2)^2(x-2)+a(x+2)^2\\ =(x+2)^2(x^2-2x+a)\)

MaxWong May 2, 2019
edited by MaxWong  May 2, 2019
 #2
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Thank you!

Guest May 2, 2019

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