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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=2x2f(x) = 2x^2\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)=2x2f(x) = 2x^2\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. Define functions: We have:\newlinef(x)=2x2f(x) = 2x^2\newlineg(x)=4x+6g(x) = 4x + 6\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)=(2x2)∗(4x+6)(f * g)(x) = (2x^2) * (4x + 6)
  3. Distribute terms: Distribute 2x22x^2 to each term in 4x+64x + 6.(f∗g)(x)=2x2∗4x+2x2∗6(f * g)(x) = 2x^2 * 4x + 2x^2 * 6
  4. Perform multiplication: Perform the multiplication. (f⋅g)(x)=8x3+12x2(f \cdot g)(x) = 8x^3 + 12x^2

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