Question

How do you factor `10x^2+15x-70`?

Answer 1

The correct factoring is `5(2x + 7)(x - 2)`

Explanation:

We can start getting rid of a `5`:

`5(2x^2 + 3x - 14)`

Now we rewrite as

`5(2x^2 - 4x + 7x - 14)`

Which is equivalent as `-4x + 7x = 3x`. Now notice that we can factor further:

`5(2x(x - 2) + 7(x - 2))`

We can now factor out `(x - 2)`.

`5(2x + 7)(x - 2)`

If we try expanding this we see

`5(2x^2 + 7x - 4x - 14)`

`10x^2 + 15x - 70`

Which is what we had at first, so the factoring is correct.

Hopefully this helps!

Answer 2

$$10x^2+15x-70=5(2x+7)(x-2)$$

Explanation:

1. Take out the common factor of 5 to give: $$5(2x^2+3x-14)$$

2. You know that the brackets will next look like this:
   $$5(2x ± ??)(x ± ??)$$

3. You need to determine what two numbers when multiplied will equal -14 and will fit in with the 2x. A quick bit of trial and error shows that the numbers that will fit are +7 and -2 which gives: $$5(2x+7)(x-2)$$