Question

Why is the factorization of `2x^2+7x+6=(2x+3)(x+2)?`

If you factor quadratics with `a gt 1` then you have to find factors of `ac` that add to give `b`. So why is the answer `2` and `3` if they don't add to give `7`?

Answer 1

`"see explanation"`

Explanation:

`"given a a quadratic in "color(blue)"standard form ";ax^2+bx+c`

`"to factor consider the factors of ac which sum to b as"`
`"you have stated above"`

`2x^2+7x+6" is in standard form"`

`"with "a=2,b=7" and "c=6`

`"the factors of the product "2xx6=12`

`"which sum to + 7 are + 4 and + 3"`

`"split the middle term using these factors"`

`2x^2+4x+3x+6larrcolor(blue)"factor by grouping"`

`=color(red)(2x)(x+2)color(red)(+3)(x+2)`

`"take out the "color(blue)"common factor "(x+2)`

`=(x+2)(color(red)(2x+3))`

`2x^2+7x+6=(x+2)(2x+3)`