How do you factor the expression #x^2 - 5x - 14#?

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Answer 1 · 2016-04-07T09:24:38

# (x + 2 ) ( x - 7) # is the factorised form of the expression.

#x^2 - 5x - 14#

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 * (- 14) = -14#

AND

#N_1 +N_2 = b = - 5#

After trying out a few numbers we get #N_1 = 2 # and #N_2 =-7#

#2*(-7) = -14#, and #2+(-7)= - 5 #

#x^2 - 5x - 14 = x^2 - 7x + 2x - 14#

# = x ( x - 7) + 2 ( x - 7)#

#(x - 7)# is a common factor to each of the terms

# (x + 2 ) ( x - 7) # is the factorised form of the expression.