How do you long divide (6x^3+5x^2+2x+12) div (2x+3)?

1 Answer
P dilip_k
Mar 4, 2016

3x^2-2x+4

Explanation:

(6x^3+5x^2+2x+12)/(2x+3)
=(3x^2(2x+3)-9x^2+5x^2+2x+12)/(2x+3)
=(3x^2(2x+3)-4x^2+2x+12)/(2x+3)
=(3x^2(2x+3)-2x(2x+3)+6x+2x+12)/(2x+3)
=(3x^2(2x+3)-2x(2x+3)+8x+12)/(2x+3)
=(3x^2(2x+3)-2x(2x+3)+4(2x+3))/(2x+3)
=(cancel(2x+3))((3x^2-2x+4))/cancel(2x+3)
3x^2-2x+4

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