How do you factor the expression #x^2 + 2x - 15#?

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Answer 1 · 2016-03-16T12:46:42

# (x -3) (x+5) # is the factorised form of the expression.

#x^2 + 2x -15#

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*(-15) = -15#

AND

#N_1 +N_2 = b = 2#

After trying out a few numbers we get #N_1 = 5# and #N_2 =-3#

#5*(-3) = -15#, and #5+(-3)= 2#

#x^2 + 2x -15 = x^2 + 5x - 3x -15#

#= x (x+5) - 3(x+5)#

#= (x -3) (x+5) # .
# (x -3) (x+5) # is the factorised form of the expression.