Q. 395 - Intermediate Algebra

Question

In the following exercises, factor completely using the difference of squares pattern, if possible.

$24p^2+ 54$

Step-by-Step Solution

Answer

The Factored form of given polynomial is, 

$6(4p^2+9)$

Step 1. Given Information

We are given a polynomial,

$24p^2+ 54$

Step 2. Factorizing the polynomial

Factoring out greatest common factor $6$, we get 

$24p^2+ 54=6(4p^2+9)$

The polynomial cannot be factorized further.

Step 3. Checking the factorization by multiplying

Multiplying the factors, we get

$$\begin{gathered} 6(4p^2+9)=24p^2+ 54 \\ 6\times 4p^2+6\times 9)=24p^2+ 54 \\ 24p^2+ 54=24p^2+ 54 \\ LHS=RHS \end{gathered}$$

Hence the factorization is correct.