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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−2x+6f(x) = -2x + 6\newlineg(x)=−xg(x) = -x\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)=−2x+6f(x) = -2x + 6\newlineg(x)=−xg(x) = -x\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. Multiply Functions: We have:\newlinef(x)=−2x+6f(x) = -2x + 6\newlineg(x)=−xg(x) = -x\newlineNow, we need to multiply these two functions to find (f∗g)(x)(f * g)(x).\newline(f∗g)(x)=(−2x+6)∗(−x)(f * g)(x) = (-2x + 6) * (-x)
  3. Distribute Terms: Distribute −x-x to each term in the polynomial −2x+6-2x + 6.(f∗g)(x)=(−2x)(−x)+(6)(−x)(f * g)(x) = (-2x)(-x) + (6)(-x)
  4. Perform Multiplication: Perform the multiplication for each term.\newline(f∗g)(x)=2x2−6x(f * g)(x) = 2x^2 - 6x
  5. Simplify Polynomial: Express your answer as a simplified polynomial.\newlineThe polynomial 2x2−6x2x^2 - 6x is already in its simplest form.

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