Factor out the greatest common factor. If the greatest common factor is 1, just retype the polynomial.

44b^5+2b^4

1 answer

To factor out the greatest common factor (GCF) from the polynomial \( 44b^5 + 2b^4 \), we first determine the GCF of the coefficients and the variable parts.

  1. Coefficients: The coefficients are \( 44 \) and \( 2 \). The GCF of \( 44 \) and \( 2 \) is \( 2 \).
  2. Variable parts: The variable parts are \( b^5 \) and \( b^4 \). The GCF of \( b^5 \) and \( b^4 \) is \( b^4 \) (the lowest power of \( b \)).

Now we can combine these to find the overall GCF:

\[ \text{GCF} = 2b^4 \]

Next, we factor \( 2b^4 \) out of each term of the polynomial:

\[ 44b^5 + 2b^4 = 2b^4(22b + 1) \]

Thus, the factored form is:

\[ \boxed{2b^4(22b + 1)} \]