How do you use the remainder theorem to determine the remainder when the polynomial $8 x^{3} + 4 x^{2} - 19$ $8x^3+4x^2-19$ is divided by $x + 2$ $x+2$ ?

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Answer 1 · 2016-12-08T08:25:13

The remainder is $= - 67$ $=-67$

If we have a polynomial $f (x)$ $f(x)$ and we divide by $(x - c)$ $(x-c)$

Then,

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

If $x = c$ $x=c$

We have, $f (c) = O + r$ $f(c)=O+r$

$r$ $r$ is the remainder

That's the remainder theorem

Here, $f (x) = 8 x^{3} + 4 x^{2} - 19$ $f(x)=8x^3+4x^2-19$

and $c = - 2$ $c=-2$

So, $f (- 2) = - 8 \cdot 8 + 4 \cdot 4 - 19 = - 64 + 16 - 19 = - 67$ $f(-2)=-8*8+4*4-19=-64+16-19=-67$

How do you use the remainder theorem to determine the remainder when the polynomial 8x3+4x2−198x^3+4x^2-19 is divided by x+2x+2?