Factorise: 3x^{2}-x-4 | vedclass

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Question

(A) Given polynomial: $3x^{2}-x-4$Comparing with the standard quadratic form $ax^{2}+bx+c$,we have $a=3$,$b=-1$,and $c=-4$.We need to find two numbers

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) Given polynomial: $3x^{2}-x-4$Comparing with the standard quadratic form $ax^{2}+bx+c$,we have $a=3$,$b=-1$,and $c=-4$.We need to find two numbers $l$ and $m$ such that $l+m = b = -1$ and $lm = a 	imes c = 3 	imes (-4) = -12$.The two numbers that satisfy these conditions are $-4$ and $3$,since $-4+3 = -1$ and $(-4) 	imes 3 = -12$.Now,split the middle term $-x$ as $-4x+3x$:$3x^{2}-4x+3x-4$Group the terms:$= x(3x-4) + 1(3x-4)$Factor out the common binomial $(3x-4)$:$= (3x-4)(x+1)$Thus,the factors are $(3x-4)(x+1)$.

Factorise: $3x^{2}-x-4$

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