Question

How do you factor the expression `15t^2 - 17t - 4`?

Answer 1

`15t^2-17t-4 = (5t+1)(3t-4)`

Explanation:

Given:

`15t^2-17t-4`

Use an AC method:

Find a pair of factors of `AC=15*4 = 60` which differ by `B=17`.

The pair `20, 3` works.

Use this pair to split the middle term and factor by grouping...

`15t^2-17t-4 = 15t^2-20t+3t-4`

`color(white)(15t^2-17t-4) = (15t^2-20t)+(3t-4)`

`color(white)(15t^2-17t-4) = 5t(3t-4)+1(3t-4)`

`color(white)(15t^2-17t-4) = (5t+1)(3t-4)`

`color(white)()`
Footnote

In the above example, we looked for a pair of factors that differed by `B=17`, since the coefficient of the constant term was negative.

If we were attempting to factor:

`15t^2-17t+4`

then we would instead look for a pair of factors of `AC=60` with sum `B=17`.

The pair `12, 5` works and hence we find:

`15t^2-17t+4 = (15t^2-12t)-(5t-4)`

`color(white)(15t^2-17t+4) = 3t(5t-4)-1(5t-4)`

`color(white)(15t^2-17t+4) = (3t-1)(5t-4)`