To factor the expression [tex]\( 49t + 7 \)[/tex], we start by identifying the greatest common factor (GCF) of the terms in the expression.
1. Identify the GCF of the coefficients in [tex]\( 49t \)[/tex] and [tex]\( 7 \)[/tex]:
- The coefficient of [tex]\( 49t \)[/tex] is 49.
- The constant term is 7.
- The GCF of 49 and 7 is 7 since 7 is the largest number that divides both 49 and 7 exactly.
2. Factor out the GCF from the expression:
- Write the expression as a product of the GCF and another factor.
- [tex]\( 49t \)[/tex] can be written as [tex]\( 7 \times 7t \)[/tex].
- [tex]\( 7 \)[/tex] can be written as [tex]\( 7 \times 1 \)[/tex].
3. Now factor out the 7:
[tex]\[
49t + 7 = 7 \times 7t + 7 \times 1
\][/tex]
[tex]\[
= 7 \left( 7t + 1 \right)
\][/tex]
Thus, the factored form of the expression [tex]\( 49t + 7 \)[/tex] is:
[tex]\[
7 \left( 7t + 1 \right)
\][/tex]
