Question

factor out the common factor 6b^5 + 10^4 - 10b^2

Answer 1

To factor the expression \( 6b^5 + 10b^4 - 10b^2 \), we first identify the common factor in each term.

The terms in the expression are:
- \( 6b^5 \)
- \( 10b^4 \)
- \( -10b^2 \)

Now, let's find the common factor:

1. The coefficients are \( 6, 10, \) and \( -10 \). The greatest common factor (GCF) of these coefficients is \( 2 \).
2. The variable part has \( b^5, b^4, \) and \( b^2 \). The lowest power of \( b \) present is \( b^2 \).

So, the overall common factor is \( 2b^2 \).

Now we factor \( 2b^2 \) out of each term:

\[
6b^5 + 10b^4 - 10b^2 = 2b^2(3b^3 + 5b^2 - 5)
\]

Thus, the factored form of the expression is:

\[
\boxed{2b^2(3b^3 + 5b^2 - 5)}
\]