Question

How do you factor `6b^2 + b - 2`?

Answer 1

`(2b-1)(3b+2)`

Explanation:

`"using the a-c method to factor the quadratic"`

`"the factors of the product "6xx-2=-12`

`"which sum to + 1 are - 3 and + 4"`

`"split the middle term using these factors"`

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

`=color(red)(3b)(2b-1)color(red)(+2)(2b-1)`

`"take out the "color(blue)"common factor "(2b-1)`

`=(2b-1)(color(red)(3b+2))`

`6b^2+b-2=(2b-1)(3b+2)`