Polynomial

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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?

Guest Jun 29, 2022

BuilderBoi · Answer 1 · 2022-06-30T12:15:08

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

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

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

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

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

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

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