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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=2x2f(x) = 2x^2\newlineg(x)=−5x+2g(x) = -5x + 2\newlineWrite your answer as a polynomial or a rational function in simplest form.\newline______

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Full solution

Q. What is (f∗g)(x)(f * g)(x)?\newlinef(x)=2x2f(x) = 2x^2\newlineg(x)=−5x+2g(x) = -5x + 2\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)=2x2f(x) = 2x^2 \newlineg(x)=−5x+2g(x) = -5x + 2 \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)∗(−5x+2)(f * g)(x) = (2x^2) * (-5x + 2)
  3. Distribute Terms: Distribute 2x22x^2 to both terms in g(x)g(x). \newline(f⋅g)(x)=2x2⋅(−5x)+2x2⋅2(f \cdot g)(x) = 2x^2 \cdot (-5x) + 2x^2 \cdot 2
  4. Perform Multiplication: Perform the multiplication.\newline(f∗g)(x)=−10x3+4x2(f * g)(x) = -10x^3 + 4x^2

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