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)