When the expression 2x^2+5x-3 is written in the equivalent form (2x-1) (x+3), list the factors

see explanation

Step-by-step explanation:

To factor the quadratic

2x² + 5x - 3

Consider the product of the factors of the coefficient of the x² term and the constant term which sum to give the coefficient of the x term.

product = 2 * - 3 = - 6 and sum = + 5

The required factors are + 6 and - 1

Use these factors to split the x - term

2x² + 6x - x - 3 (factor the first/second and third / fourth terms)

= 2x (x + 3) - 1 (x + 3) ← factor out (x + 3)

= (x + 3) (2x - 1)

The factors are (x + 3) and (2x - 1)