# Evaluate f(x)⋅g(x) by modeling or by using the distributive property. f(x)=(−3x+2) and g(x)=(2x^{2}−5x−1)

Evaluate f(x)⋅g(x) by modeling or by using the distributive property.
$f\left(x\right)=\left(-3x+2\right)\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}g\left(x\right)=\left(2{x}^{2}-5x-1\right)$
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Let's use the distributive property.
$f\left(x\right)\cdot g\left(x\right)=\left(-3x+2\right)\left(2{x}^{2}-5x-1\right)=\left(-3x+2\right)×2{x}^{2}-\left(-3x+2\right)×5x-\left(-3x+2\right)×1\phantom{\rule{0ex}{0ex}}=-3x×2{x}^{2}+2×{2}^{2}-\left(-3\right)x×5x-2×5x-\left(-3\right)x×1-2×1\phantom{\rule{0ex}{0ex}}=\left(-3\ast 2\right){x}^{3}+4{x}^{2}+\left(3×5\right){x}^{2}-10x+3x-2\phantom{\rule{0ex}{0ex}}=-6{x}^{3}+4{x}^{2}+15{x}^{2}-10x+3x-2=-6{x}^{3}+\left(4+15\right){x}^{2}+\left(-10+3\right)\left(x-2\right)$
$x=-6{x}^{3}+19{x}^{2}-7x-2$