How do you divide (2x^3+7x^2-5x-4) / (2x+1)2x3+7x2−5x−42x+1 using polynomial long division?

2 Answers
Cem Sentin
Jun 15, 2018

Quotient is x^2+3x-4x2+3x−4 and remainder is 00

Explanation:

2x^3+7x^2-5x-42x3+7x2−5x−4

=2x^3+x^2+6x^2+3x-8x-42x3+x2+6x2+3x−8x−4

=x^2*(2x+1)+3x*(2x+1)-4*(2x+1)x2⋅(2x+1)+3x⋅(2x+1)−4⋅(2x+1)

=(2x+1)*(x^2+3x-4)(2x+1)⋅(x2+3x−4)

Hence quotient is x^2+3x-4x2+3x−4 and remainder is 00

Tony B
Jun 15, 2018

x^2+3x-4 x2+3x−4

Explanation:

Numerator ->color(white)("d")2x^3+7x^2-5x-4→d2x3+7x2−5x−4
color(magenta)(x^2)(2x+1)-> color(white)("d")ul(2x^3+x^2larr" Subtract"
color(white)("dddddddddddddd") 0+6x^2-5x-4
color(magenta)(3x)(2x+1)-> color(white)("dddddd") ul(6x^2+3xlarr" Subtract")
color(white)("ddddddddddddddddddd")0-8x-4
color(magenta)(-4)(2x+1) ->color(white)("ddddddd.d")ul(-8x-4 larr" Subtract")
"Remainder"-> color(white)("ddddddddddd")0color(white)("d")+0

color(white)("dddddddddddddd")color(magenta)( x^2+3x-4 )

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