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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−2xf(x) = -2x\newlineg(x)=−4x+6g(x) = -4x + 6\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)=−2xf(x) = -2x\newlineg(x)=−4x+6g(x) = -4x + 6\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. Calculate Product: We have:\newlinef(x)=−2xf(x) = -2x\newlineg(x)=−4x+6g(x) = -4x + 6\newlineNow, calculate the product of f(x)f(x) and g(x)g(x).\newline(f∗g)(x)=(−2x)∗(−4x+6)(f * g)(x) = (-2x) * (-4x + 6)
  3. Distribute −2x-2x: Distribute −2x-2x across the terms in the parentheses.\newline(f∗g)(x)=(−2x∗−4x)+(−2x∗6)(f * g)(x) = (-2x * -4x) + (-2x * 6)
  4. Perform Multiplication: Perform the multiplication. (f⋅g)(x)=8x2−12x(f \cdot g)(x) = 8x^2 - 12x
  5. Simplify Polynomial: Express your answer as a simplified polynomial.\newlineThe polynomial 8x2−12x8x^2 - 12x is already in its simplest form.

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