How do you factor # x^2 - 9x + 14 #?

Question

29761 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-05-24T03:45:56

# x^2 - 9x + 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 = -9#

After trying out a few numbers we get #N_1 = -2# and #N_2 =-7#
#(-2).(-7) = 14#, and #(-2)+(-7)= -9#

# x^2 - 9x + 14 = x^2 - 7x - 2x + 14#

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

#=color(green)((x-7)(x-2)#