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If (x + 2)(3x^2 + x + 5) = Ax^2 + Bx^2 + Cx + D, what is the value of A + B - C - D?

 Jun 29, 2022
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\((x+2)(3x^2 + x + 5) \)

\(x(3x^2 + x + 5) + 2(3x^2 + x + 5)\)

\(x(3x^2 + x + 5) = 3x^3 + x^2 + 5x\)

\(2(3x^2 + x + 5) = 6x^2 + 2x + 10\)

\((6x^2 + 2x + 10) + (3x^3 + x^2 + 5x) = 3x^3 + 7x^2 + 7x + 10\)

\(3 + 7 - 7 - 10 = \color{brown}\boxed{-7}\)

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 Jun 30, 2022

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