For what value of c will the polynomial $P (x) = - 2 x^{3} + c x^{2} - 5 x + 2$ $P(x)=-2x^3+cx^2-5x+2$ have the same remainder when it is divided by x-2 and x+1?

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For what value of c will the polynomial $P (x) = - 2 x^{3} + c x^{2} - 5 x + 2$ $P(x)=-2x^3+cx^2-5x+2$ have the same remainder when it is divided by x-2 and x+1?

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Answer 1 · 2017-01-08T20:25:38

$c = 11$ $c = 11$

Explanation:

The remainder theorem states that when a polynomial $p (x)$ $p(x)$ is divided by $x - a$ $x - a$ , the remainder is given by $p (a)$ $p(a)$ .

Thus, the remainder when $P (x)$ $P(x)$ is divide by $x - 2$ $x - 2$ is $- 2 {(2)}^{3} + c {(2)}^{2} - 5 (2) + 2 = - 16 + 4 c - 10 + 2 = - 24 + 4 c$ $-2(2)^3 + c(2)^2 - 5(2) + 2 = -16 + 4c - 10 + 2 = -24 + 4c$

The remainder when $P (x)$ $P(x)$ is divided by $x + 1$ $x + 1$ is $- 2 {(- 1)}^{3} + c {(- 1)}^{2} - 5 (- 1) + 2 = 2 + c + 5 + 2 = 9 + c$ $-2(-1)^3 + c(-1)^2 - 5(-1) + 2 = 2 + c + 5 + 2 = 9 + c$

Setting the two as being equal, we have:

$- 24 + 4 c = 9 + c$ $-24 + 4c = 9 + c$

$3 c = 33$ $3c = 33$

$c = 11$ $c = 11$

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For what value of c will the polynomial $P (x) = - 2 x^{3} + c x^{2} - 5 x + 2$ $P(x)=-2x^3+cx^2-5x+2$ have the same remainder when it is divided by x-2 and x+1?

1 Answer

Explanation:

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For what value of c will the polynomial P(x)=−2x3+cx2−5x+2P(x)=-2x^3+cx^2-5x+2 have the same remainder when it is divided by x-2 and x+1?

1 Answer

Explanation:

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For what value of c will the polynomial $P (x) = - 2 x^{3} + c x^{2} - 5 x + 2$ $P(x)=-2x^3+cx^2-5x+2$ have the same remainder when it is divided by x-2 and x+1?