How do you factor completely: #2x^2-10x+12#?

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Answer 1 · 2015-07-28T06:30:45

# color(blue)((2)(x-2)(x-3)# is the factorised form.

# 2x^2−10x+12#

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 = 2*12 =24#
and
#N_1 +N_2 = b = -10#

After trying out a few numbers we get #N_1 = -6# and #N_2 =-4#
#(-6)*(-4) = 24#, and #-6+(-4)=-10#

# 2x^2−10x+12 = 2x^2−6x -4x+12#

# =2x(x-3) -4(x-3)#

Here, #(x-3)# is common to both terms:

# =(2x-4)(x-3) #
Also, #2# is common to both terms of the first bracket

# color(blue)(2(x-2)(x-3)# is the factorised form.