Question

Determine the factors of 5x2 + 29x − 6.

(5x − 1)(x + 6)
(5x − 6)(x + 1)
(5x − 3)(x + 2)
(5x − 2)(x + 3)

Answer 1

To factor the quadratic expression \( 5x^2 + 29x - 6 \), we can use the method of splitting the middle term or the trial-and-error method with the given choices.

First, let's check each option by multiplying the factors to see if they give the original expression.

1. **Option (5x - 1)(x + 6)**:
\[
(5x - 1)(x + 6) = 5x^2 + 30x - x - 6 = 5x^2 + 29x - 6
\]
This matches our original expression.

2. **Option (5x - 6)(x + 1)**:
\[
(5x - 6)(x + 1) = 5x^2 + 5x - 6x - 6 = 5x^2 - x - 6
\]
This does not match.

3. **Option (5x - 3)(x + 2)**:
\[
(5x - 3)(x + 2) = 5x^2 + 10x - 3x - 6 = 5x^2 + 7x - 6
\]
This does not match.

4. **Option (5x - 2)(x + 3)**:
\[
(5x - 2)(x + 3) = 5x^2 + 15x - 2x - 6 = 5x^2 + 13x - 6
\]
This does not match.

Based on the calculations, the only correct factorization of \( 5x^2 + 29x - 6 \) from the options provided is:

\[
\boxed{(5x - 1)(x + 6)}
\]