Question

How do you factor the trinomial `t^2 + 6tf - 16f^2`?

Answer 1

`(t-2f)(t+8f)`

Explanation:

If `at^2+btf+cf^2` is the trinomial, we have to split `b` in two parts, which add up to `b` and whose product is `ac`.

Here, in `t^2+6tf-16f^2`, we will have to spit `6` in two parts, so that the product of the two is `-16`.

It is apparent that these are `+8` and `-2` and hence `t^2+6tf-16f^2` can be written as

`t^2+8tf-2tf-16f^2` or

= `t(t+8f)-2(t+8f)` or

= `(t-2f)(t+8f)`