Question

How do you factor $6x^2+5x-6$?

Answer 1

Find the factors:

For the equation $a{x}^2+bx+c$, first multiply $a$ and $c$, then find two factors such that their sum or difference will be equal to $b$.

$6x^2+5x-6$

$$\begin{gathered} \Rightarrow 6x^2+(9-4)x-6 \\ \Rightarrow 6x^2+9x-4x-6 \\ \Rightarrow 3x(2x+3)-2(2x+3) \\ \Rightarrow (2x+3)(3x-2) \end{gathered}$$

Hence, factors of $6x^2+5x-6$ are $(2x+3)$ and $(3x-2)$.