To factor the polynomial [tex]\( p^2 + 4p - 7p - 28 \)[/tex] by grouping, follow these detailed steps:
1. Separate the polynomial into two groups: Group the terms to simplify the factoring process. In this case, we can group the terms as:
[tex]\[
(p^2 + 4p) + (-7p - 28)
\][/tex]
2. Factor out the greatest common factor (GCF) from each group:
- In the first group, [tex]\( p^2 + 4p \)[/tex], the GCF is [tex]\( p \)[/tex]:
[tex]\[
p(p + 4)
\][/tex]
- In the second group, [tex]\( -7p - 28 \)[/tex], the GCF is [tex]\( -7 \)[/tex]:
[tex]\[
-7(p + 4)
\][/tex]
3. Rewrite the polynomial with the factored groups:
[tex]\[
p(p + 4) - 7(p + 4)
\][/tex]
4. Factor out the common binomial factor [tex]\( (p + 4) \)[/tex] from both terms:
[tex]\[
(p + 4)(p - 7)
\][/tex]
Therefore, the polynomial [tex]\( p^2 + 4p - 7p - 28 \)[/tex] factors to:
[tex]\[
(p - 7)(p + 4)
\][/tex]
So, the final solution is:
[tex]\[
p^2 + 4p - 7p - 28 = (p - 7)(p + 4)
\][/tex]
