To factor the expression [tex]\( 28ac - 63a + 4c - 9 \)[/tex] by grouping, follow these detailed steps:
1. Group the terms: Separate the expression into two groups.
[tex]\[
(28ac - 63a) + (4c - 9)
\][/tex]
2. Factor out the greatest common factor (GCF) from each group:
- In the first group [tex]\( 28ac - 63a \)[/tex], the GCF is [tex]\( 7a \)[/tex]:
[tex]\[
28ac - 63a = 7a(4c - 9)
\][/tex]
- In the second group [tex]\( 4c - 9 \)[/tex], there is no common factor to factor out, so it remains as is:
[tex]\[
4c - 9
\][/tex]
So, the expression now looks like this:
[tex]\[
7a(4c - 9) + (4c - 9)
\][/tex]
3. Factor out the common binomial factor [tex]\( 4c - 9 \)[/tex] from both terms:
[tex]\[
(4c - 9)(7a + 1)
\][/tex]
Therefore, the factored form of the expression [tex]\( 28ac - 63a + 4c - 9 \)[/tex] is:
[tex]\[
(7a + 1)(4c - 9)
\][/tex]
