How do you factor the expression #x^2 + 4x – 32#?

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Answer 1 · 2016-06-19T09:17:28

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

#x^2 + 4 x - 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 = 4#

After trying out a few numbers we get #N_1 = 8# and #N_2 =-4#
#8*(-4) = -32#, and #8+(-4)= 4#

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

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

#= color(blue)( (x -4) ( x + 8 ) #