Question

6x² + 3x - 9
which of the expressions below matches with the equation above? (graph it and check it or look at the picture, how it is done!)
-3 (2x + 3) (x - 1)
3 (2x + 3) (x - 1)
2 (3x - 1) (x - 2)
3 (2x + 3) (x + 4)

Explanation:

Step1: Factor out GCF

First, identify and factor out the greatest common factor (GCF) of all terms. The GCF of $6x^2$, $3x$, and $-9$ is 3.

$$\begin{align*} 6x^2 + 3x - 9 &= 3(2x^2 + x - 3) \end{align*}$$

Step2: Factor quadratic trinomial

Factor the quadratic $2x^2 + x - 3$ by finding two numbers that multiply to $2\times(-3)=-6$ and add to 1. These numbers are 3 and -2. Split the middle term and factor by grouping:

$$\begin{align*} 2x^2 + x - 3 &= 2x^2 + 3x - 2x - 3 \\ &= x(2x + 3) - 1(2x + 3) \\ &= (2x + 3)(x - 1) \end{align*}$$

Step3: Combine factors

Substitute the factored quadratic back into the expression from Step1:

$$\begin{align*} 6x^2 + 3x - 9 &= 3(2x + 3)(x - 1) \end{align*}$$

Answer:

3 (2x + 3) (x - 1)