Question

How do you factor `14y^2+15y-9`?

Answer 1

`color(blue)(( 7y-3) (2y+3)` is the factorised form of the expression.

Explanation:

`14y^2+15y−9`

We can Split the Middle Term of this expression to factorise it.

In this technique, if we have to factorise an expression like `ay^2 + by + c`, we need to think of 2 numbers such that:

`N_1*N_2 = a*c = 14*-9 = -126`
and,
`N_1 +N_2 = b = 15`

After trying out a few numbers we get `N_1 = 21` and `N_2 =-6`
`21*(-6) = -126`, and `21+(-6)= 15`

`14y^2+color(blue)(15y)−9 = 14y^2+color(blue)(21y -6y)−9`

`= 7y(2y+3) -3 (2y +3)`

`color(blue)(( 7y-3) (2y+3)` is the factorised form of the expression.