How do you factor the trinomial #x^2-12x+32#?

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Answer 1 · 2015-11-23T16:05:58

#color(blue)((x-4)(x-8) # is the factorised form of the expression.

#x^2-12x+32#

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 = 1*32 =32#
AND
#N_1 +N_2 = b = -12#

After trying out a few numbers we get:

#N_1 = -8# and #N_2 =-4#

#(-8)*(-4) = 32#, and

#(-8) +(-4)= -12#

#x^2-color(blue)(12x)+32 = x^2color(blue)(-8x-4x)+32#

# =x(x-8) - 4(x-8)#

#(x-8)# is a common factor to each of the terms.

#color(blue)((x-4)(x-8) # is the factorised form of the expression.