Factorise 12 x^{3} + 17 x^{2} + 3 x - 2. | vedclass

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Question

(A) Let $p(x) = 12x^3 + 17x^2 + 3x - 2$.By the Factor Theorem,we test values to find a root. Let $x = -1$:$p(-1) = 12(-1)^3 + 17(-1)^2 + 3(-1) - 2 = -

Vedclass · Accepted Answer

$(x+1)(4x-1)(3x+2)$

Vedclass · Answer

(A) Let $p(x) = 12x^3 + 17x^2 + 3x - 2$.By the Factor Theorem,we test values to find a root. Let $x = -1$:$p(-1) = 12(-1)^3 + 17(-1)^2 + 3(-1) - 2 = -12 + 17 - 3 - 2 = 0$.Since $p(-1) = 0$,$(x+1)$ is a factor.Now,divide $12x^3 + 17x^2 + 3x - 2$ by $(x+1)$ using long division or synthetic division:$12x^3 + 17x^2 + 3x - 2 = (x+1)(12x^2 + 5x - 2)$.Next,factorize the quadratic $12x^2 + 5x - 2$ by splitting the middle term:$12x^2 + 8x - 3x - 2 = 4x(3x + 2) - 1(3x + 2) = (4x - 1)(3x + 2)$.Thus,the complete factorization is $(x+1)(4x-1)(3x+2)$.

Factorise $12 x^{3} + 17 x^{2} + 3 x - 2$.

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