How do you factor #x² + 14x + 40#?

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Answer 1 · 2015-07-04T15:33:17

#color(green)(=(x+4)(x+10) #

#x^2 + 14x +40#

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*40 = 40#
and,
#N_1 +N_2 = b = 14#

After trying out a few numbers we get #N_1 = 10# and #N_2 =4#
#10*4 = 40#, and #10 + 4= 14#

#x^2 + 14x +40 =x^2 + color(green)(10x + 4x) +40 #

#=x(x+10) + 4(x+10) #
Here #(x+10) # is common to both terms.

So the factorised form is#color(green)(=(x+4)(x+10) #