Question

Which of the following polynomials has a remainder of 24 when divided by x+2?

Answer 1

Option C is the correct choice   $-2x^4+4x^2+3x-2$,

Remainder of a polynomial by substitution

For a polynomial f(x) to give a remainder of 24 when divided by x + 2:

f(-2) = 24

By testing, substitute x = -2 into the equation $-2x^4+4x^2+3x-2$

$f(x) = -2x^3+4x^2+3x-2\\\\f(-2)=-2(-2)^3+4(-2)^2+3(-2)-2\\\\f(-2)=-2(-8)+4(4)-6-2\\\\f(-2)=16+16-8\\\\f(-2)=32-8\\\\f(-2)=24$

Since f(-2) = 24 when x = -2 is substituted into  $-2x^4+4x^2+3x-2$, then  $-2x^4+4x^2+3x-2$ has a remainder of 24 when divided by x+2

Learn more on remainder of a polynomial here: brainly.com/question/24202892

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