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

2 Answers
Oct 22, 2017

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!

Oct 22, 2017

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)