factor 5r^2+9r - 18?

Answer 1

When meeting the expressions of power 2, like this one.
We let y(r) = 5r ^ 2 + 9r - 18
One can first find the roots of the equation y(r) = 0, by using a calculator, or by hand if you'd like:
Delta = 9 ^ 2 - 4 * 5 * (-18) = 441
r = [-9 +/- SquareRoot(Delta)] / (10) = [-9 +/- 21] / 10 = -3 or 1.2 = 6/5
Now, say y(r) = 0 has two solutions r = a, and r = b, then y(r) can be factorred to A(r - a)(r - b), where A is some constant.
So, we have:
5r ^ 2 + 9r - 18 = A (r + 3)(r - 6/5)
If we expand (r + 3)(r - 6/5), we will have r ^ 2 + something, but originally, we have 5r ^ 2 + something, so we must multiply the (r + 3)(r - 6/5) by 5, i.e A = 5. So:
5r ^ 2 + 9r - 18 = 5 (r + 3)(r - 6/5) = [5 (r - 6/5)] (r + 3) = (5r - 6) (r + 3)

Answer 2

(5r - 6)(r + 3)

Answer 3

(5r - 6)*(r + 3)