Q 31E - Intermediate Algebra

Question

In the following exercises, factor the greatest common factor from each polynomial.

$-4p^3 q - 12p^2 q^2 + 16p{q}^2$

Step-by-Step Solution

Answer

The simplest polynomial is

$4pq(-p^2-3pq+4q)$.

Step 1. Given

A polynomial is given as $-4p^3 q - 12p^2 q^2 + 16p{q}^2$ 

Step 2. Concept Used.

First we have to find the GCF (group common factor). Now, rewrite the given polynomial using GCF and apply the distributive property to factor the expression.

Step 3. Calculation.

A polynomial is given as $-4p^3 q - 12p^2 q^2 + 16p{q}^2$

GCF of the polynomial,

$$\begin{gathered} 4p^{3}q=2\times 2\times p\times p\times p\times q \\ 12p^2{q}^2=2\times 2\times 3\times p\times p\times q\times q \\ 16p{q}^2=2\times 2\times 2\times 2\times p\times q\times q \\ GCF=2\times 2\times p\times q \\ =4pq \end{gathered}$$

Step 4. Simplifying the polynomial.

$$\begin{gathered} -4p^3 q - 12p^2 q^2 + 16p{q}^2 \\ =4pq(-p^2)-4pq\left(3pq\right)+4pq\left(q\right) \\ =4pq(-p^2-3pq+4q) \end{gathered}$$

Step 5. Check the solution.

Check by multiplying the factors.

$4pq(-p^2-3pq+4q)=-4p^3 q - 12p^2 q^2 + 16p{q}^2$

Which holds true.