How do you factor out 5x2 5x-10?

Answer 1

I assume you mean 5x2+5x-10 in my answer:

When factoring ax2+bx+c, find two numbers which multiply to give a*c and add to give b.

In this case, a*c = -50 and b = 5

So the two numbers are 10 and -5.

Now, rewrite the middle term with these two coefficients:

5x2 + 10x - 5x - 10 (Notice it's the same expression because 10x - 5x = 5x as in the original)

We can factor the first half: 5x2 + 10x as 5x(x + 2)

Then, we factor the second half: -5x - 10 (don't forget the signs in front) as -5(x + 2)

We rewrite the original now as 5x(x+2) - 5(x+2)

But then we have (x+2) as a factor of both term, so we take it out the front:

(x+2)(5x - 5) and this is the factored form.

You could proceed further to 5(x+2)(x-1) if required by extracting the 5 from the second term.