How do you divide $(x^3+8x^2-3x+16)div(x^2+5)$ using long division?

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Answer 1 · 2018-01-12T10:27:43

The quotient is $=(x+8)$ and the remainder is $=-(8x+24)$

Perform the long division

$color(white)(aaaa)$ $x^3+8x^2-3x+16$ $color(white)(aaaa)$ $|$ $x^2+5$

$color(white)(aaaa)$ $x^3+0x^2+5x$ $color(white)(aaaaaaaa)$ $|$ $x+8$

$color(white)(aaaaa)$ $0+8x^2-8x+16$

$color(white)(aaaaaaa)$ $+8x^2+0x+40$

$color(white)(aaaaaaaaa)$ $+0-8x-24$

Therefore,

$(x^3+8x^2-3x+16)/(x^2+5)=(x+8)-(8x+24)/(x^2+5)$

The quotient is $=(x+8)$ and the remainder is $=-(8x+24)$

How do you divide (x^3+8x^2-3x+16)div(x^2+5)(x^3+8x^2-3x+16)div(x^2+5) using long division?