To factorize the expression [tex]\( 6^2 - 5Qb + 25 \)[/tex] by finding any common monomial factors, let's go through each term separately.
1. Evaluate [tex]\( 6^2 \)[/tex]:
[tex]\[
6^2 = 36
\][/tex]
2. Rewrite the expression with the evaluated term:
[tex]\[
36 - 5Qb + 25
\][/tex]
Next, let's examine each term to see if there is a common monomial factor that can be factored out. We'll look for the greatest common factor (GCF) of the coefficients as well as the variables.
### Step-by-Step Process
1. Identify the coefficients:
- The coefficients in the expression are 36, -5, and 25.
2. Find the GCF of the coefficients:
- The factors of 36 are: [tex]\( 1, 2, 3, 4, 6, 9, 12, 18, 36 \)[/tex]
- The factors of -5 are: [tex]\( 1, 5 \)[/tex]
- The factors of 25 are: [tex]\( 1, 5, 25 \)[/tex]
- The greatest common factor among these coefficients is 1.
3. Check the variables:
- The first term is a constant (36), so it has no variables.
- The second term is [tex]\( -5Qb \)[/tex].
- The third term is a constant (25).
Since none of the terms have common variables that appear in every term, and the GCF of the coefficients is 1, there is no common monomial factor that can be factored out from the entire expression.
### Simplification:
The expression [tex]\( 36 - 5Qb + 25 \)[/tex] cannot be factored further by extracting a common monomial factor because there is no single monomial that is common to all terms.
Therefore, the simplified form of the expression remains:
[tex]\[
36 - 5Qb + 25
\][/tex]
