How do you divide $(x^2-5x-5x^3+x^4)div(5+x)$ using synthetic division?

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Answer 1 · 2016-12-05T08:13:05

The remainder is $=1300$ and the quotient is $=x^3-10x^2+51x-260$

Rearrange the polynomials in decreasing powers of $x$

Let's do the long division

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

$color(white)(aaaa)$ $x^4+5x^3$ $color(white)(aaaaaaaaaaaaa)$ $∣$ $x^3-10x^2+51x-260$

$color(white)(aaaa)$ $0-10x^3+x^2$

$color(white)(aaaaaa)$ $-10x^3-50x^2$

$color(white)(aaaaaaaaaa)$ $0+51x^2-5x$

$color(white)(aaaaaaaaaaaa)$ $+51x^2+255x$

$color(white)(aaaaaaaaaaaaaaaa)$ $0-260x$

$color(white)(aaaaaaaaaaaaaaaaaa)$ $-260x-1300$

$color(white)(aaaaaaaaaaaaaaaaaaaaaaa)$ $0+1300$

You can use the remainder theorem

$f(x)=x^4-5x^3+x^2-5x$

$f(-5)=625+625+25+25=1300$

How do you divide (x^2-5x-5x^3+x^4)div(5+x)(x^2-5x-5x^3+x^4)div(5+x) using synthetic division?