To determine the factors of the polynomial [tex]\(5x^2 + 39x - 8\)[/tex], we look for expressions of the form [tex]\((ax + b)(cx + d)\)[/tex] that multiply to give the original polynomial.
After analyzing the options, we find that the correct factorization of the polynomial [tex]\(5x^2 + 39x - 8\)[/tex] is:
[tex]\[
(x + 8)(5x - 1)
\][/tex]
Let's verify this by expanding the factors:
[tex]\[
(x + 8)(5x - 1) = x \cdot 5x + x \cdot (-1) + 8 \cdot 5x + 8 \cdot (-1)
\][/tex]
Simplify each term separately:
[tex]\[
= 5x^2 - x + 40x - 8
\][/tex]
Combine like terms:
[tex]\[
= 5x^2 + 39x - 8
\][/tex]
This confirms that:
[tex]\[
(x + 8)(5x - 1) = 5x^2 + 39x - 8
\][/tex]
Thus, the correct factorization of the given polynomial is:
[tex]\[
(5x - 1)(x + 8)
\][/tex]
So, the correct answer is:
[tex]\[
(5 x - 1)(x + 8)
\][/tex]
