How do you use polynomial long division to divide $(5x^4-3x^3+2x^2-1)div(x^2+4)$ and write the polynomial in the form $p(x)=d(x)q(x)+r(x)$ ?

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Answer 1 · 2017-05-04T06:58:27

The answer is $5x^4-3x^3+2x^2-1=(5x^2-3x-18)(x^2+4)+(12x+71)$

Let's perform the long division

$color(white)(aaaa)$ $5x^4-3x^3+2x^2$ $color(white)(aaaa)$ $-1$ $color(white)(aaaa)$ $|$ $x^2+4$

$color(white)(aaaa)5x^4color(white)(aaaaa)+20x^2color(white)(aaaaaaaaaaa)|5x^2-3x-18$

$color(white)(aaaaaa)$ $0-3x^3-18x^2$

$color(white)(aaaaaaaa)$ $-3x^3+$ $color(white)(aaa)$ $-12x$

$color(white)(aaaaaaaaaa)$ $+0-18x^2$ $color(white)(aa)$ $+12x-1$

$color(white)(aaaaaaaaaaaaa)$ $-18x^2$ $color(white)(aaaaaa)$ $-72$

$color(white)(aaaaaaaaaaaaaa)$ $+0+12x$ $color(white)(aaaaaa)$ $+71$

Therefore,

$5x^4-3x^3+2x^2-1=(5x^2-3x-18)(x^2+4)+(12x+71)$

How do you use polynomial long division to divide (5x^4-3x^3+2x^2-1)div(x^2+4)(5x^4-3x^3+2x^2-1)div(x^2+4) and write the polynomial in the form p(x)=d(x)q(x)+r(x)p(x)=d(x)q(x)+r(x)?