Question

Is it possible to factor `y=4x^2+19x - 5`? If so, what are the factors?

Answer 1

`y=(x+5)(4x-1)`

Explanation:

Factor:

`y=4x^2+19x-5`

You can factor the right-hand side by using the "splitting the middle term" method.

Multiply the coefficient of the first term by the constant.

`4xx-5=-20`

Find two numbers that when added equal `-19`, which is the coefficient of the middle term, and that multiply to `-20`. The numbers `20` and `-1` meet the requirements.

Split `19x` as the sum of `20x` and `-x`.

`y=4x^2+20x-x-5`

Factor out the common terms in the first two terms and the second two terms.

`y=4x(x+5)-(x+5)`

It is understood that `-(x+5)` is `-1(x+5)`.

Factor out the common term `x+5`.

`y=(x+5)(4x-1)`