Question

Use factor to factorise 6x3 + 17x2 + 4x - 12 completely

Answer 1

$Let \: p(x) = 6x^{3} + 17x^{2} + 4x - 12$

$\implies p(x) = 6x^{3} + 12x^{2} + 5x^{2} + 10x - 6x -12$

$= 6x^{2} (x+2) + 5x(x+2) - 6(x+2) \\= (x+2)(6x^{2}+5x-6)\\= (x+2)[ 6x^{2} + 9x - 4x - 6 ] \\= (x+2) [3x(2x+3)-2(2x+3) ]\\= (x+2)((2x+3)(3x-2)$

Therefore.,

$\red { Factorisation \: of \: 6x^{3} + 17x^{2} + 4x - 12}$

$\green { = (x+2)((2x+3)(3x-2)}$

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Answer 2

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