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Simplify (x+1)(2x+3)(3x+4) = (6x^{2}+5)(x-3)$ to the form $0 = Ax^{2}+Bx+C, where A, B, and C are positive integers with a greatest common divisor of 1. What is A+B+C?

 May 13, 2019
 #1
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Just to reformat your question for my aesthetic quick;

 

Simplify \((x+1)(2x+3)(3x+4) = (6x^{2}+5)(x-3)\) to the form \(0 = Ax^{2}+Bx+C\) where A, B, and C are positive integers with a greatest common divisor of 1. What is \(A+B+C\)?

 

\((x+1)(2x+3)(3x+4) = (6x^{2}+5)(x-3)\)

\((2x^2+3x+2x+3)(3x+4) = 6x^3-18x^2+5x-15\)

\((2x^2+5x+3)(3x+4)=6x^3-18x^2+5x-15\)

\(6x^3+8x^2+15x^2+20x+9x+12=6x^3-18x^2+5x-15\)

\(6x^3+23x^2+29x+12=6x^3-18x^2+5x-15\)

\(41x^2+24x+27=0\)

\(Ax^2 + Bx + C = 0\)

\(A = 41, B = 24, C = 27\)

\(A + B + C = 41+24+27=92\)

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 May 14, 2019

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