Question

How do you factor `v^2-7v+10`?

Answer 1

Notice that `10 = 5 xx 2` and `7 = 5 + 2`, so

`v^2-7v+10 = (v-5)(v-2)`

When you are faced with a quadratic like this whose first coefficient is `1`, look for factors of the constant term and see if their sum or difference is equal to the middle coefficient. This is often a quick way to find a factorisation.

Answer 2

`f(v) = v^2 - 7v + 10 = (v - p)(v - q)`

Find 2 numbers, sum (-7) and product (10). They are -2 and -5.

`f(v) = (v - 2)(v - 5)`