To factor the expression [tex]\( 35q + 28 \)[/tex], we need to look for the greatest common factor (GCF) of the terms involved.
1. Identify the coefficients and constants:
The expression [tex]\( 35q + 28 \)[/tex] consists of the terms [tex]\( 35q \)[/tex] and [tex]\( 28 \)[/tex].
2. Find the GCF of the coefficients:
- The coefficient of [tex]\( q \)[/tex] is 35.
- The constant term is 28.
We now find the GCF of 35 and 28.
- The prime factorization of 35 is [tex]\( 5 \times 7 \)[/tex].
- The prime factorization of 28 is [tex]\( 2^2 \times 7 \)[/tex].
The common prime factor is 7. Hence, the GCF of 35 and 28 is 7.
3. Factor out the GCF:
We factor 7 out of each term in the expression:
[tex]\[
35q + 28 = 7 \times 5q + 7 \times 4
\][/tex]
4. Rewrite the expression:
Group the factored terms and combine:
[tex]\[
35q + 28 = 7(5q + 4)
\][/tex]
Thus, the expression [tex]\( 35q + 28 \)[/tex] is factored as [tex]\( 7(5q + 4) \)[/tex].
