The quadratic formula is a pain in the ass to use, especially if you're doing it by hand. It's usually faster and easier to look at the polynomial and see if you can figure out the factors, rather than just immediately going to the quadratic formula.
E.G.:
5x2 - 17x + 6
You're looking for factors of 5 that when multiplied with factors of 6 will add up to 17. We know we're looking for a sum and not a difference because the sign of the constant term (the 6 in this instance) is positive. So,
5 * 3
+ 1 * 2 17
Now that we know the factors, we just need to ensure that the signs match up. The end result is:
(5x - 2)(x - 3)
r3+3r2-54r
Let's just look at r
2 + 3r - 54 since that's the important part. Since the sign of the constant term (54) is negative, we're looking for factors of 1 that when multiplied with factors of 54 the result differs by three.
1 * 6
- 1 * 9 -3
That we got -3 here is mostly irrelevant since if you change the order you'll end up with +3. The important thing is that the factors differ by 3. Now that we know them, it's just making sure the signs are correct. The result is:
(r + 9)(r - 6)
With the final answer being r(r + 9)(r - 6).
You're probably not practiced enough for this advice to apply to you, but if you're looking at a quadratic and it's not immediately apparent what the factors are, use the quadratic formula. And then if you are practiced enough where this does apply to you, you'll probably plug it into a calculator or a computer. Arithmetic is tedious as hell.