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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−3x+6f(x) = -3x + 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)=−3x+6f(x) = -3x + 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)=−3x+6f(x) = -3x + 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)=(−3x+6)∗(2x)(f * g)(x) = (-3x + 6) * (2x)
  3. Perform Multiplication: Perform the multiplication using the distributive property (also known as the FOIL method for binomials): \newline(f∗g)(x)=−3x∗2x+6∗2x(f * g)(x) = -3x * 2x + 6 * 2x
  4. Simplify Expression: Simplify the expression by performing the multiplication: (f⋅g)(x)=−6x2+12x(f \cdot g)(x) = -6x^2 + 12x
  5. Final Polynomial: Express your answer as a simplified polynomial.\newlineThe final simplified form of the polynomial is:\newline(f⋅g)(x)=−6x2+12x(f \cdot g)(x) = -6x^2 + 12x

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