Question

Factor out the greatest common factor. If the greatest common factor is 1, just retype the polynomial.
15b5c9–5b4c10+40bc9

Answer 1

To factor out the greatest common factor (GCF) from the polynomial \( 15b^5c^9 - 5b^4c^{10} + 40bc^9 \), we first identify the GCF of the coefficients and the variable parts.

1. **Coefficients**: The coefficients are 15, -5, and 40. The GCF of these numbers is 5.

2. **Variable \( b \)**: The variable terms are \( b^5 \), \( b^4 \), and \( b \). The GCF is \( b^1 \) (or simply \( b \)).

3. **Variable \( c \)**: The variable terms are \( c^9 \), \( c^{10} \), and \( c^9 \). The GCF is \( c^9 \).

Now, we can combine these factors:

\[
\text{GCF} = 5bc^9
\]

Next, we factor \( 5bc^9 \) out of each term in the original polynomial:

1. \( 15b^5c^9 \div 5bc^9 = 3b^4 \)
2. \( -5b^4c^{10} \div 5bc^9 = -b^3c \)
3. \( 40bc^9 \div 5bc^9 = 8 \)

Putting it all together, we have:

\[
15b^5c^9 - 5b^4c^{10} + 40bc^9 = 5bc^9(3b^4 - b^3c + 8)
\]

Thus, the factored form of the polynomial is:

\[
\boxed{5bc^9(3b^4 - b^3c + 8)}
\]