Polynomial long division

Question

asked Oct 25, 2020 212k views

1 Answer

Xudong Zhang · Answer 1 · 2020-10-30T21:21:06+0000

You're dividing
2x^3-2x^2+3x-4 (1) by
x+1 (2).

$2x^3=2x^2\cdot x$ , and
2x^2(x+1)=2x^3+2x^2 (3). Subtract this from (1) to get a remainder of

(2x^3-2x^2+3x-4)-(2x^3+2x^2)=-2x^2+3x+4 (4)

$-2x^2=-2x\cdot x$ , and
-2x(x+1)=-2x^2-2x (5). Subtract this from (4) to get a new remainder of

(-2x^2+3x+4)-(-2x^2-2x)=5x+4 (6)

$5x=5\cdot x$ , and
5(x+1)=5x+5 (7). Subtract this from (6) to get a new remainder of

(5x+4)-(5x+5)=-1 (8)

doesn't contain any factors of
, so we're done and we've shown

(2x^3-2x^2+3x-4)/(x+1)=2x^2+(-2x^2+3x+4)/(x+1)

(2x^3-2x^2+3x-4)/(x+1)=2x^2-2x+(5x+4)/(x+1)

$(2x^3-2x^2+3x-4)/(x+1)=2x^2-2x+5-\frac1{x+1}$

so that the quotient is
2x^2-2x+5 (9).