How do you divide $(5x^3 – 6 – 5x) ÷ (10 + 5x)$ ?

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Answer 1 · 2017-08-04T16:54:06

The remainder is $=-36$ and the quotient is $=x^2-2x+3$

We perform a long division

$color(white)(aaaa)$ $5x+10$ $color(white)(aaaa)$ $|$ $5x^3+0x^2-5x-6$ $color(white)(aaaa)$ $|$ $x^2-2x+3$

$color(white)(aaaaaaaaaaaaaaaa)$ $5x^3+10x^2$

$color(white)(aaaaaaaaaaaaaaaaaa)$ $0-10x^2-5x$

$color(white)(aaaaaaaaaaaaaaaaaaaa)$ $-10x^2-20x$

$color(white)(aaaaaaaaaaaaaaaaaaaaaa)$ $-0+15x-6$

$color(white)(aaaaaaaaaaaaaaaaaaaaaaaaaa)$ $+15x+30$

$color(white)(aaaaaaaaaaaaaaaaaaaaaaaaaaaa)$ $+0-36$

The remainder is $=-36$ and the quotient is $=x^2-2x+3$

$(5x^3-5x-6)/(5x+10)=x^2-2x+3-36/(5x+10)$

How do you divide (5x^3 – 6 – 5x) ÷ (10 + 5x)(5x^3 – 6 – 5x) ÷ (10 + 5x)?