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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−5x+6f(x) = -5x + 6\newlineg(x)=−2xg(x) = -2x\newlineWrite your answer as a polynomial or a rational function in simplest form.\newline______

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Q. What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−5x+6f(x) = -5x + 6\newlineg(x)=−2xg(x) = -2x\newlineWrite your answer as a polynomial or a rational function in simplest form.\newline______
  1. Identify formula: Identify the formula for (f∗g)(x)(f * g)(x).(f∗g)(x)(f * g)(x) is the product of f(x)f(x) and g(x)g(x).(f∗g)(x)=f(x)∗g(x)(f * g)(x) = f(x) * g(x)
  2. Given functions: We have: \newlinef(x)=−5x+6f(x) = -5x + 6 \newlineg(x)=−2xg(x) = -2x \newlineTo find (f∗g)(x)(f * g)(x), we need to multiply f(x)f(x) by g(x)g(x).\newline(f∗g)(x)=(−5x+6)∗(−2x)(f * g)(x) = (-5x + 6) * (-2x)
  3. Multiply functions: Now, distribute −2x-2x to each term in the polynomial −5x+6-5x + 6.
    (f∗g)(x)=(−5x∗−2x)+(6∗−2x)(f * g)(x) = (-5x * -2x) + (6 * -2x)
  4. Distribute terms: Perform the multiplication for each term.\newline(f∗g)(x)=10x2−12x(f * g)(x) = 10x^2 - 12x

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