Question

Factor out the greatest common factor. If the greatest common factor is 1, just retype the polynomial.
18w^5–2w^3

Answer 1

To factor out the greatest common factor from the expression \( 18w^5 - 2w^3 \), we first need to identify the common factor in both terms.

1. The coefficients are 18 and -2. The greatest common factor (GCF) of 18 and 2 is 2.
2. The variable parts are \( w^5 \) and \( w^3 \). The GCF of \( w^5 \) and \( w^3 \) is \( w^3 \).

Combining these, the greatest common factor of the entire expression is \( 2w^3 \).

Now, we can factor out \( 2w^3 \) from the original polynomial:

\[
18w^5 - 2w^3 = 2w^3(9w^2 - 1)
\]

So the factored form of the polynomial is:

\[
2w^3(9w^2 - 1)
\]