# Write the cubic polynomial function f(x) in expanded form with zeros 4, -2, and 1, given that f(-1)=-12

Write the cubic polynomial function f(x) in expanded form with zeros 4, -2, and 1, given that f(-1)=-12
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Piper Pruitt
Given that $f\left(-1\right)=-12$
The cubic polynomial function is
$f\left(x\right)=k\left(x-a\right)\left(x-b\right)\left(x-c\right)$
where $a=-4,b=-2,c=1\phantom{\rule{0ex}{0ex}}f\left(x\right)=k\left(x+4\right)\left(x+2\right)\left(x-1\right)\phantom{\rule{0ex}{0ex}}f\left(-1\right)=k\left(-1+4\right)\left(-1+2\right)\left(-1-1\right)\phantom{\rule{0ex}{0ex}}-12=k\left(3\right)\left(1\right)\left(-2\right)\phantom{\rule{0ex}{0ex}}-12=-6k\phantom{\rule{0ex}{0ex}}k=2$
put the value in equation
$f\left(x\right)=2\left[\left(x+4\right)\left(x+2\right)\left(x-1\right)\right]\phantom{\rule{0ex}{0ex}}=2\left[\left({x}^{2}+2x+4x+8\right)\left(x-1\right)\right]\phantom{\rule{0ex}{0ex}}=2\left[{x}^{3}+5{x}^{2}+2x-8\right]\phantom{\rule{0ex}{0ex}}f\left(x\right)=2{x}^{3}+10{x}^{2}+4x-16$