Question

How do you factor `6x^2+17x+12`?

Answer 1

`6x^2+17x+12=(2x+3)(3x+4)`

Explanation:

In `6x^2+17x+12`, split the middle term so that the product of the two coefficients is equal to product of the coefficients of first and third term.

As product of coefficients of first and third term is `6xx12=72`, `17x` can be split into `8x` and `9x`. Hence

`6x^2+17x+12=6x^2+8x+9x+12`

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

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