How do you divide $2y^3+y^2-5y+2$ by $y+2$ ?

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Answer 1 · 2017-08-13T13:00:04

$(2y^3+y^2-5y+2)/(y+2) = 2y^2-3y+1$

We can split the terms of the dividend into multiples of the divisor as follows:

$2y^3+y^2-5y+2=2y^3+4y^2-3y^2-6y+y+2$

$color(white)(2y^3+y^2-5y+2)=2y^2(y+2)-3y(y+2)+1(y+2)$

$color(white)(2y^3+y^2-5y+2)=(2y^2-3y+1)(y+2)$

So:

$(2y^3+y^2-5y+2)/(y+2) = 2y^2-3y+1$

How do you divide 2y^3+y^2-5y+22y^3+y^2-5y+2 by y+2y+2?