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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−3xf(x) = -3x\newlineg(x)=−5x+5g(x) = -5x + 5\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)=−3xf(x) = -3x\newlineg(x)=−5x+5g(x) = -5x + 5\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. Calculate Product: We have:\newlinef(x)=−3xf(x) = -3x\newlineg(x)=−5x+5g(x) = -5x + 5\newlineNow, calculate the product of f(x)f(x) and g(x)g(x).\newline(f∗g)(x)=(−3x)∗(−5x+5)(f * g)(x) = (-3x) * (-5x + 5)
  3. Distribute −3x-3x: Distribute −3x-3x across the terms in g(x)g(x).(f⋅g)(x)=(−3x⋅−5x)+(−3x⋅5)(f \cdot g)(x) = (-3x \cdot -5x) + (-3x \cdot 5)
  4. Perform Multiplication: Perform the multiplication. (f⋅g)(x)=15x2−15x(f \cdot g)(x) = 15x^2 - 15x
  5. Express Answer: Express your answer as a simplified polynomial.\newlineThe polynomial 15x2−15x15x^2 - 15x is already in its simplest form.

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