How do you factor $6x^2-11x+4$ ?

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Answer 1 · 2015-08-11T16:34:40

$color(blue)((3x-4)(2x-1)$ is the factorised form of the expression.

$6x^2−11x+4$

We can Split the Middle Term of this expression to factorise it.

In this technique, if we have to factorise an expression like $ax^2 + bx + c$ , we need to think of 2 numbers such that:

$N_1*N_2 = a*c = 6*4 = 24$
and
$N_1 +N_2 = b = -11$

After trying out a few numbers we get $N_1 = -8$ and $N_2 =-3$
$(-8)*(-3) = 24$ and $-8+(-3)= -11$

$6x^2−color(blue)(11x)+4 =6x^2−color(blue)(3x-8x)+4$

$=6x^2−color(blue)(3x-8x)+4$

$=3x(2x-1) -4(2x-1)$
$color(blue)((3x-4)(2x-1)$ is the factorised form of the expression.

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