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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−3x2+10xf(x) = -3x^2 + 10x\newlineg(x)=xg(x) = x\newlineWrite your answer as a polynomial or a rational function in simplest form.\newline______

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Add and subtract functionsright chevron icon

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Q. What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−3x2+10xf(x) = -3x^2 + 10x\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. Define functions: We have:\newlinef(x)=−3x2+10xf(x) = -3x^2 + 10x\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)=(−3x2+10x)∗x(f * g)(x) = (-3x^2 + 10x) * x
  3. Multiply functions: Distribute xx to each term in the polynomial −3x2+10x-3x^2 + 10x.
    (f∗g)(x)=(−3x2∗x)+(10x∗x)(f * g)(x) = (-3x^2 * x) + (10x * x)
  4. Distribute xx: Perform the multiplication for each term.(f∗g)(x)=−3x3+10x2(f * g)(x) = -3x^3 + 10x^2

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