How do you factor the trinomial #8 + 6x + x^2#?

1 Answer
Mar 25, 2018

#x^2 + 6x + 8 = (x+4)(x+2)#

Explanation:

Consider the quadratic equation #ax^2 + bx + c#

We want to factorize it and express it in the form #(x-k)(x-h)# where k and h are the two roots. If we expand #(x-k)(x-h)# we get #x^2-kx-hx+kh# which can be simplified to #x^2-(k+h)x+kh#
This looks very much like the form #ax^2 + bx + c#

We essentially want to find two numbers that when multiplied give us c (#kh#), and when added give us b (#k+h#).

The factors of 8 are 1, 2, and 4.
#2 times 4=8#
note that 2 + 4 = 6 which is the coefficient for x.

Since the numbers 2 and 4 when multiplied equal c and when added equal b they can be used to factorize the expression.

#x^2 + 6x + 8 = (x+4)(x+2)#