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What is (q*s)(x) ? {:[q(x)=5x+2],[s(x)=-4x+5]:} Write your answer as a polynomial or a ratior ◻

What is (q∗s)(x)?(q*s)(x) ?\newline q(x)=5x+2q(x)=5x+2 \newlines(x)=−4x+5s(x)=-4x+5\newlineWrite your answer as a polynomial or a rational function.\newline◻

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Composition of linear and quadratic functions: find an equationright chevron icon

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Q. What is (q∗s)(x)?(q*s)(x) ?\newline q(x)=5x+2q(x)=5x+2 \newlines(x)=−4x+5s(x)=-4x+5\newlineWrite your answer as a polynomial or a rational function.\newline◻
  1. Identify functions: Identify the functions to be multiplied. q(x)=5x+2q(x) = 5x + 2 s(x)=−4x+5s(x) = -4x + 5
  2. Multiply functions: Multiply the functions q(x)q(x) and s(x)s(x).(q∗s)(x)=(5x+2)(−4x+5)(q*s)(x) = (5x + 2)(-4x + 5)
  3. Distribute terms: Distribute each term in the first polynomial to each term in the second polynomial.\newline(q∗s)(x)=5x∗(−4x)+5x∗5+2∗(−4x)+2∗5(q*s)(x) = 5x*(-4x) + 5x*5 + 2*(-4x) + 2*5
  4. Simplify expression: Simplify the expression by performing the multiplications.\newline(q∗s)(x)=−20x2+25x−8x+10(q*s)(x) = -20x^2 + 25x - 8x + 10
  5. Combine like terms: Combine like terms.\newline(q∗s)(x)=−20x2+17x+10(q*s)(x) = -20x^2 + 17x + 10

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