Factor out the greatest common factor. $$ -36 p^{3}+20 p^{2}+12 p $$

Question

UpStudy AI · Accepted Answer

To factor out the greatest common factor (GCF) from the expression:

$$
-36 p^{3} + 20 p^{2} + 12 p
$$

**Step 1: Find the GCF of the coefficients**

The coefficients are $$-36$$, $$20$$, and $$12$$.

- **Factors of 36**: $$2^2 \times 3^2$$
- **Factors of 20**: $$2^2 \times 5$$
- **Factors of 12**: $$2^2 \times 3$$

The common factor among the coefficients is $$2^2 = 4$$.

**Step 2: Find the GCF of the variables**

The variable terms are $$p^3$$, $$p^2$$, and $$p$$.

The smallest power of $$p$$ common to all terms is $$p$$.

**Step 3: Combine the GCFs**

The overall GCF is $$4p$$.

**Step 4: Factor out the GCF**

$$
-36 p^{3} + 20 p^{2} + 12 p = 4p \left( -9 p^{2} + 5 p + 3 \right)
$$

So, the factored form is:

$$
4p (-9p^2 + 5p + 3)
$$

**Final Answer:**

$$
4p\,(-9\,p^{2} + 5\,p + 3)
$$
The greatest common factor is $$4p$$, and the expression factored is $$4p(-9p^2 + 5p + 3)$$.

Factor out the greatest common factor. \[ -36 p^{3}+20 p^{2}+12 p \]