To factor the polynomial [tex]\( x^3 + 11x^2 - 3x - 33 \)[/tex] by grouping, follow these steps:
1. Group the terms in pairs:
[tex]\[
(x^3 + 11x^2) + (-3x - 33)
\][/tex]
2. Factor out the greatest common factor (GCF) from each pair of terms:
- For the first pair [tex]\( x^3 + 11x^2 \)[/tex], the GCF is [tex]\( x^2 \)[/tex].
[tex]\[
x^2(x + 11)
\][/tex]
- For the second pair [tex]\( -3x - 33 \)[/tex], the GCF is [tex]\( -3 \)[/tex].
[tex]\[
-3(x + 11)
\][/tex]
3. Combine the factored forms:
[tex]\[
x^2(x + 11) - 3(x + 11)
\][/tex]
Thus, the correct way to determine the factors by grouping is:
[tex]\[
x^2(x + 11) - 3(x + 11)
\][/tex]
So, the correct option is:
[tex]\[
x^2(x + 11) - 3(x + 11)
\][/tex]
