To factor the polynomial [tex]\(20b^2 + 5b\)[/tex], we can follow these steps:
1. Identify the Greatest Common Factor (GCF):
- First, look at the coefficients (20 and 5). The GCF of 20 and 5 is 5.
- Next, look at the variables in each term. Both terms have a common variable, [tex]\(b\)[/tex].
Combining these, the GCF of [tex]\(20b^2\)[/tex] and [tex]\(5b\)[/tex] is [tex]\(5b\)[/tex].
2. Factor out the GCF:
- Write each term as a product of the GCF and another factor.
- For the term [tex]\(20b^2\)[/tex]:
[tex]\[
20b^2 = 5b \cdot 4b
\][/tex]
- For the term [tex]\(5b\)[/tex]:
[tex]\[
5b = 5b \cdot 1
\][/tex]
3. Express the polynomial as a product:
- Now, factor [tex]\(5b\)[/tex] out of each term:
[tex]\[
20b^2 + 5b = 5b(4b) + 5b(1)
\][/tex]
- Use the distributive property to factor [tex]\(5b\)[/tex] out:
[tex]\[
20b^2 + 5b = 5b(4b + 1)
\][/tex]
Therefore, the factored form of the polynomial [tex]\(20b^2 + 5b\)[/tex] is [tex]\(5b(4b + 1)\)[/tex].
