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

Question
Equations and inequalities
Evaluate f(x)⋅g(x) by modeling or by using the distributive property.
$$\displaystyle{f{{\left({x}\right)}}}={\left(−{3}{x}+{2}\right)}{\quad\text{and}\quad}{g{{\left({x}\right)}}}={\left({2}{x}^{{{2}}}−{5}{x}−{1}\right)}$$

2020-10-19
Let's use the distributive property.
PSKf(x)⋅g(x)=(−3x+2)(2x^{2} −5x−1) =(-3x+2)\times 2x^{2}-(-3x+2)\times 5x-(-3x+2)\times 1 =-3x\times 2x^{2}+2\times 2^{2}-(-3)x\times 5x-2\times 5x-(-3)x\times 1-2\times 1 =(-3*2)x^{3}+4x^{2}+(3\times 5)x^{2}-10x+3x-2 =-6x^{3}+4x^{2}+15x^{2}-10x+3x-2 =-6x^{3}+(4+15)x^{2}+(-10+3)x-2ZSK
$$\displaystyle{x}=-{6}{x}^{{{3}}}+{19}{x}^{{{2}}}-{7}{x}-{2}$$

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