Question

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

Answer 1

`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)`