Question

How do you factor `2y^2+7y+5`?

Answer 1

`(2y+5)(y+1)`

`2y^2` only has `y` and `2y` as factors

Similarly 5 only has factors 1 and 5

Answer 2

`2y^2+7y+5=color(blue)((2y+5)+(y+1)`

Explanation:

Factor:

`2y^2+7y+5`

Use the `"ac"` method to factor this trinomial. `a=2` and `c=5`

Multiply `2` by `5` to get `10`. Find two numbers that when added equal `7` and when multiplied equal `10`. The numbers `5` and `2` meet the requirements.

Split the middle term `7y` to `5y+2y`. This method is also sometimes called "splitting the middle term."

`2y^2+5y+2y+5`

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

`y(2y+5)+(2y+5)` `larr` understood to be `1(2y+5)`

Factor out the common term `(2y+5)`.

`(2y+5)+(y+1)`