How do you use long division to divide $(2x^3-4x^2-15x+5)/(x-1)^2$ ?

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Answer 1 · 2017-01-15T07:22:02

The answer is $=2x-((17x-5))/((x^2-2x+1))$

Let 's do the long division

$color(white)(aaaa)$ $2x^3-4x^2-15x+5$ $color(white)(aaaa)$ $∣$ $color(red)(x^2-2x+1)$

$color(white)(aaaa)$ $2x^3-4x^2+2x$ $color(white)(aaaaaaaaa)$ $∣$ $color(blue)(2x)$

$color(white)(aaaaaaa)$ $0-0-17x+5$

Therefore,

$(2x^3-4x^2-15x+5)/(x^2-2x+1)=2x-((17x-5))/((x^2-2x+1))$

How do you use long division to divide (2x^3-4x^2-15x+5)/(x-1)^2(2x^3-4x^2-15x+5)/(x-1)^2?