Question

How do you factor `2x^2-98`?

Answer 1

`2(x-7)(x+7)`

Explanation:

There's a common factor of 2 for both terms, so let's pull that out:
`2(x^2 - 49)`

Now, we know that `49 = 7^2`, which means that we can use difference of squares! The difference of squares formula is
`a^2 - b^2 = (a-b)(a+b)`

With `a = x` and `b = 7`, this tells us that
`x^2 - 49 = x^2 - 7^2 = (x-7)(x+7)`

so our final factorization is
`2x^2 - 98 = 2(x-7)(x+7)`