How do you factor completely: #8x^2 − 11x + 3#?

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Answer 1 · 2015-07-17T07:27:47

# = color(blue)((8x-3)(x-1)#

#8x^2−11x+3#

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 = 8*3 = 24#
and
#N_1 +N_2 = b = -11#

After trying out a few numbers we get:
#N_1 = -3# and #N_2 =-8#

#(-3)*(-8) = 24# and
#(-3)+(-8)=-11#

#8x^2−11x+3 = 8x^2−8x - 3x+3#

#8x(x-1) -3 (x-1)#

# = color(blue)((8x-3)(x-1)#