Question

3x² - 23x - 36
answer
greatest common factor difference of perfect squares
trinomial factoring none of the above

Explanation:

Step1: Identify polynomial type

The expression $3x^2 - 23x - 36$ is a quadratic trinomial (3 terms, degree 2).

Step2: Rule out other methods

• GCF: No common factor across all terms.
• Difference of squares: Requires 2 terms, not 3.

Step3: Test trinomial factoring

Find two numbers: product $3\times(-36)=-108$, sum $-23$. The numbers are $-27$ and $4$.
Rewrite and factor:

$$\begin{align*} 3x^2 -27x +4x -36&=3x(x-9)+4(x-9)\\ &=(3x+4)(x-9) \end{align*}$$

Factoring is successful.

Answer:

Trinomial Factoring