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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=2x2−7xf(x) = 2x^2 - 7x\newlineg(x)=−5xg(x) = -5x\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)=2x2−7xf(x) = 2x^2 - 7x\newlineg(x)=−5xg(x) = -5x\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)=2x2−7xf(x) = 2x^2 - 7x\newlineg(x)=−5xg(x) = -5x\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)=(2x2−7x)∗(−5x)(f * g)(x) = (2x^2 - 7x) * (-5x)
  3. Multiply functions: Distribute −5x-5x to each term in 2x2−7x2x^2 - 7x.\newline(f∗g)(x)=2x2∗(−5x)+(−7x)∗(−5x)(f * g)(x) = 2x^2 * (-5x) + (-7x) * (-5x)
  4. Distribute terms: Perform the multiplication for each term.\newline(f∗g)(x)=−10x3+35x2(f * g)(x) = -10x^3 + 35x^2

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