To factor the quadratic polynomial [tex]\(3h^2 - 11h - 42\)[/tex] completely, we need to find the factors of the form [tex]\((ah + b)(ch + d)\)[/tex] that multiply together to give the original polynomial.
Given the polynomial [tex]\(3h^2 - 11h - 42\)[/tex], the correct factorization is:
[tex]\[ (h - 6)(3h + 7) \][/tex]
Let's verify it:
1. Multiply the factors:
[tex]\[
(h - 6)(3h + 7)
\][/tex]
2. Use the distributive property (FOIL method) to expand:
[tex]\[
= h \cdot 3h + h \cdot 7 - 6 \cdot 3h - 6 \cdot 7
\][/tex]
[tex]\[
= 3h^2 + 7h - 18h - 42
\][/tex]
3. Combine like terms:
[tex]\[
= 3h^2 - 11h - 42
\][/tex]
This matches the original quadratic polynomial, confirming that the factorization is correct. Therefore, the correct answer is:
A. [tex]\((3h + 7)(h - 6)\)[/tex]
