How do you use the remainder theorem to determine the remainder when the polynomial $2 x^{3} + 3 x^{2} - 5 x + 2$ $2x^3+3x^2-5x+2$ is divided by $x + 2$ $x+2$ ?

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Answer 1 · 2017-02-21T09:00:03

$8$ $8$

The remainder theorem states that a polynomial $P (x)$ $P(x)$ is divided by $(x - a)$ $(x-a)$ the remainder is $P (a)$ $P(a)$

so for $P (x) = 2 x^{3} + 3 x^{2} - 5 x + 2$ $P(x)=2x^3+3x^2-5x+2$

the remainder on dividing by $(x + 2) is P (- 2)$ $(x+2) " is " P(-2)$

$P (- 2) = 2 {(- 2)}^{3} + 3 {(- 2)}^{2} - 5 (- 2) + 2$ $P(-2)=2(-2)^3+3(-2)^2-5(-2)+2$

$P (- 2) = 2 \times - 8 + 3 \times 4 + 10 + 2$ $P(-2)=2xx-8+3xx4+10+2$

$P (- 2) = - 16 + 12 + 10 + 2 = 8$ $P(-2)=-16+12+10+2=8$

How do you use the remainder theorem to determine the remainder when the polynomial 2x3+3x2−5x+22x^3+3x^2-5x+2 is divided by x+2x+2?