How do you use the remainder theorem to determine the remainder when the polynomial $3 x^{3} - 12 x - 2$ $3x^3-12x-2$ is divided by $x + 2$ $x+2$ ?

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Answer 1 · 2017-03-08T07:29:13

$- 2 .$ $-2.$

The Remainder Theorem : If a poly. $P (x)$ $P(x)$ is divided by $(a x + b),$ $(ax+b),$

the remainder is $P (- \frac{b}{a}) .$ $P(-b/a).$

Accordingly, the remainder $= 3 {(- 2)}^{3} - 12 (- 2) - 2 = - 24 + 24 - 2 = - 2 .$ $=3(-2)^3-12(-2)-2=-24+24-2=-2.$

How do you use the remainder theorem to determine the remainder when the polynomial 3x3−12x−23x^3-12x-2 is divided by x+2x+2?