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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=3x2+10xf(x) = 3x^2 + 10x\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)=3x2+10xf(x) = 3x^2 + 10x\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)=3x2+10xf(x) = 3x^2 + 10x\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)=(3x2+10x)∗(2x)(f * g)(x) = (3x^2 + 10x) * (2x)
  3. Multiply functions: Distribute 2x2x to each term in the polynomial 3x2+10x3x^2 + 10x.
    (f∗g)(x)=2x∗3x2+2x∗10x(f * g)(x) = 2x * 3x^2 + 2x * 10x
  4. Distribute terms: Perform the multiplication for each term.\newline(f∗g)(x)=6x3+20x2(f * g)(x) = 6x^3 + 20x^2

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