Question

How do you factor completely `12y^2+9y+8y+6`?

Answer 1

Factor by grouping to find:

`12y^2+9y+8y+6 = (3y+2)(4y+3)`

Explanation:

`12y^2+9y+8y+6`

`=(12y^2+9y)+(8y+6)`

`=3y(4y+3)+2(4y+3)`

`= (3y+2)(4y+3)`

Note that the hard work / fun has already been done for you in the split `9y+8y`. Normally you would be given a quadratic like `12y^2+17y+6` to factor and have to find the split yourself.

If you are given something like `12y^2+17y+6` to factor, then one way is to multiply `12 xx 6 = 72` then try to find a pair of factors that multiply to give `72` and sum to give `17`. Once you find the pair `9`, `8` works then you can split `17y=9y+8y` and factor by grouping as we have done here.