Question

How do you factor `3x^2 − x − 4`?

Answer 1

`3x^2-x-4=(x+1)(3x-4)`

Explanation:

To factorize `3x^2-x-4`

first multiply coefficient of `x^2` and constant term. As they are `3` and `-4` respectively, their product is `-12`

Now split `-12` in two parts whose sum is equal to coefficient of `x` i.e. `-1`. Here they will be `-4` and `3`

Hence `3x^2-x-4`

= `3x^2-4x+3x-4`

= `x(3x-4)+1(3x-4)`

= `(x+1)(3x-4)`

Answer 2

`(x+1)(3x-4)`

Explanation:

`"factor using the a-c method"`

`"the factors of the product "3xx-4=-12`
`"which sum to - 1 are + 3 and - 4"`

`"split the middle term using these factors"`

`rArr3x^2+3x-4x-4larrcolor(blue)"factor in groups"`

`rArrcolor(red)(3x)(x+1)color(red)(-4)(x+1)`

`"take out the common factor "(x+1)`

`=(x+1)(color(red)(3x-4))`

`rArr3x^2-x-4=(x+1)(3x-4)`