Using the remainder theorem,find the remainde | vedclass

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Question

(A) According to the remainder theorem,if a polynomial $p(x)$ is divided by $(x - a)$,the remainder is $p(a)$.Here,the divisor is $x + 4$,which can be

Vedclass · Accepted Answer

$80$

Vedclass · Answer

(A) According to the remainder theorem,if a polynomial $p(x)$ is divided by $(x - a)$,the remainder is $p(a)$.Here,the divisor is $x + 4$,which can be written as $x - (-4)$.Therefore,$a = -4$.Now,substitute $x = -4$ into the polynomial $p(x) = x^3 + x^2 - 26x + 24$:$p(-4) = (-4)^3 + (-4)^2 - 26(-4) + 24$$p(-4) = -64 + 16 + 104 + 24$$p(-4) = -64 + 144$$p(-4) = 80$.Thus,the remainder is $80$.

Using the remainder theorem,find the remainder when the polynomial $p(x) = x^3 + x^2 - 26x + 24$ is divided by the divisor $x + 4$.

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