How do you divide $(-4x^3-15x^2-4x-12)/(x-4)$ ?

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Answer 1 · 2018-07-20T05:49:19

The remainder is $=-524$ and the quotient is $=-4x^2-31x-128$

Let's perform the synthetic division

$color(white)(aaaa)$ $4$ $|$ $color(white)(aaaa)$ $-4$ $color(white)(aaaa)$ $-15$ $color(white)(aaaaaa)$ $-4$ $color(white)(aaaaa)$ $-12$

$color(white)(aaaaa)$ $|$ $color(white)(aaaa)$ $color(white)(aaaaaaa)$ $-16$ $color(white)(aaaa)$ $-124$ $color(white)(aaaa)$ $-512$

$color(white)(aaaaaaaaa)$ _________

$color(white)(aaaaaa)$ $|$ $color(white)(aaaa)$ $-4$ $color(white)(aaaa)$ $-31$ $color(white)(aaaa)$ $-128$ $color(white)(aaaa)$ $color(red)(-524)$

The remainder is $=-524$ and the quotient is $=-4x^2-31x-128$

ALSO,

Apply the remainder theorem

When a polynomial $f(x)$ is divided by $(x-c)$ , we get

$f(x)=(x-c)q(x)+r$

Let $x=c$

Then,

$f(c)=0+r$

Here,

$f(x)=-4x^3-15x^2-4x-12$

Therefore,

$f(4)=-4*4^3-15*4^2-4*4-12$

$=-256-240-16-12$

$=-524$

The remainder is $=-524$

How do you divide (-4x^3-15x^2-4x-12)/(x-4) (-4x^3-15x^2-4x-12)/(x-4) ?