To factor the polynomial [tex]\( 5b - 15c \)[/tex] completely, follow these steps:
1. Identify the common factor:
Both terms in the polynomial [tex]\( 5b - 15c \)[/tex] contain a common factor of [tex]\( 5 \)[/tex].
2. Factor out the greatest common divisor (GCD):
Factor out [tex]\( 5 \)[/tex] from each term to simplify the polynomial. Divide every term by [tex]\( 5 \)[/tex]:
[tex]\[
5b - 15c = 5(b) - 5(3c)
\][/tex]
3. Write the polynomial in its factored form:
Now that we have factored out the [tex]\( 5 \)[/tex], we write the simplified expression within parentheses:
[tex]\[
5(b - 3c)
\][/tex]
Therefore, the completely factored form of the polynomial [tex]\( 5b - 15c \)[/tex] is:
[tex]\[
5(b - 3c)
\][/tex]
