Question

How do you factor the expression `6x^2+14x+4`?

Answer 1

`2(x+2)(3x+1)`

Explanation:

`6x^2+14x+4`

first factor out the GCF using the distributive property:

`2(3x^2+7x+2)`

Factor by grouping, we need a pair of numbers whose sum is `7` and product is `3*2=6` it is immediately clear that `1` and `6` will work, so replace the `7x` with `6x+1x`

`2(3x^2+7x+2)`

`2(3x^2+6x+x+2)`

now factor:

`2(3x(x+2)+1(x+2))`

now factor out the `(x+2)`:

`2(x+2)(3x+1)`