How do you write #x^2-x-42# in factored form?

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Answer 1 · 2015-09-16T16:17:32

#color(blue)((x+6)(x-7)# is the factorised form of the expression.

#x^2−x−42#

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*-42 = -42#
AND
#N_1 +N_2 = b = -1#

After trying out a few numbers we get #N_1 = -7# and #N_2 =6#
#-7*6 = -42# and #-7+6=-1#

#x^2−x−42=x^2−7x+6x−42#

#=x(x-7)+ 6(x-7)#

#=color(blue)((x+6)(x-7)#