To factor by grouping the expression [tex]\( 24t^2 + 18t - 4t - 3 \)[/tex], we can follow these steps:
1. Group the terms:
Group the terms in such a way that we can factor out a common factor from each group.
[tex]\[
(24t^2 + 18t) + (-4t - 3)
\][/tex]
2. Factor out the common factor from each group:
- From the first group [tex]\( (24t^2 + 18t) \)[/tex], factor out the greatest common factor, which is [tex]\( 6t \)[/tex]:
[tex]\[
24t^2 + 18t = 6t(4t + 3)
\][/tex]
- From the second group [tex]\( (-4t - 3) \)[/tex], factor out the greatest common factor, which is [tex]\(-1\)[/tex]:
[tex]\[
-4t - 3 = -1(4t + 3)
\][/tex]
Now the expression looks like this:
[tex]\[
6t(4t + 3) - 1(4t + 3)
\][/tex]
3. Factor out the common binomial factor:
Both terms contain the common factor [tex]\( (4t + 3) \)[/tex]. Factor this out:
[tex]\[
[6t - 1](4t + 3)
\][/tex]
Thus, the factored form of the expression [tex]\( 24t^2 + 18t - 4t - 3 \)[/tex] is:
[tex]\[
(6t - 1)(4t + 3)
\][/tex]
So, the final factored result is:
[tex]\[
(6t - 1)(4t + 3)
\][/tex]
