Question

# Evaluate f(x)⋅g(x) by modeling or by using the distributive property. f(x)=(−3x+2) and g(x)=(2x2−5x−1)

Modeling
$$\displaystyle f{{\left({x}\right)}}⋅ g{{\left({x}\right)}}\\={\left(-{3}{x}+{2}\right)}{\left({2}{x}^{2}-{5}{x}-{1}\right)}\\={\left(-{3}{x}+{2}\right)}⋅{2}{x}^{2}-{\left(-{3}{x}+{2}\right)}⋅{5}{x}-{\left(-{3}{x}+{2}\right)}⋅{1}\\=-{3}{x}⋅{2}{x}^{2}+{2}⋅{2}{x}^{2}-{\left(-{3}\right)}{x}⋅{5}{x}-{2}⋅{5}{x}-{\left(-{3}\right)}{x}⋅{1}-{2}⋅{1}\\={\left(-{3}⋅{2}\right)}{x}^{3}+{4}{x}^{2}+{\left({3}⋅{5}\right)}{x}^{2}-{10}{x}+{3}{x}-{2}\\=-{6}{x}^{3}+{4}{x}^{2}+{15}{x}^{2}-{10}{x}+{3}{x}-{2}\\=-{6}{x}^{3}+{\left({4}+{15}\right)}{x}^{2}+{\left(-{10}+{3}\right)}{x}-{2}\\=-{6}{x}{3}+{19}{x}{2}-{7}{x}-{2}$$