Option C is the correct choice [tex]-2x^4+4x^2+3x-2[/tex],
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 [tex]-2x^4+4x^2+3x-2[/tex]
[tex]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[/tex]
Since f(-2) = 24 when x = -2 is substituted into [tex]-2x^4+4x^2+3x-2[/tex], then [tex]-2x^4+4x^2+3x-2[/tex] has a remainder of 24 when divided by x+2
Learn more on remainder of a polynomial here: https://brainly.com/question/24202892
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