Question

How do you factor the expression `t ^2 - 11t + 30`?

Answer 1

`(t - 5)(t - 6)`

Explanation:

Looking at the expression we notice that:

(i) the coefficient of `t^2` is 1
(ii) the constant term is positive while the coefficient of `t` is negative

Therefore to factorize the expression we need to find factors of the constant (30) that sum to the coefficient of `t` (11). Then take the negative of these factors in our factorization.

The factors of 30 that sum to 11 are 6 and 5. Hence the expression factorizes as:

`(t - 5)(t - 6)`