Question

How do you factor completely: `2x^2 − 28x + 98`?

Answer 1

Separate out the common scalar factor, then spot a perfect square trinomial to find:

`2x^2-28x+98 = 2(x^2-14x+49) = 2(x-7)^2`

Explanation:

First separate out the common scalar factor `2` to get:

`2x^2-28x+98 = 2(x^2-14x+49)`

Then note that `x^2-14x+49` is a perfect square trinomial:

It is of the form `a^2-2ab+b^2 = (a-b)^2` with `a=x` and `b=7`

So `x^2-14x+49 = x^2-(2*x*7)+7^2 = (x-7)^2`