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.