By factor theorem, show that (x + 3) and (2x - 1) are the factors of 2x² + 5x - 3.

By factor theorem, (x - a) is a factor of f(x), if f(a) = 0.

f(x) = 2x² + 5x - 3

(x + 3) = (x - (-3)) is a factor of f(x), if f(-3) = 0

f(-3) = 2(-3)² + 5(-3) - 3
= 2(9) - 15 - 3
= 18 - 18 = 0

2x - 1 = 2(x - $\dfrac{1}{2}$) is a factor of f(x), if f($\dfrac{1}{2}$) = 0

$f\big(\dfrac{1}{2}\big) = 2\big(\dfrac{1}{2}\big)^2 + 5\big(\dfrac{1}{2}\big) - 3 \\[1em] = 2\big(\dfrac{1}{4}\big) + \dfrac{5}{2} - 3 \\[1em] = \dfrac{1}{2} + \dfrac{5}{2} - 3 \\[1em] = 3 - 3 = 0$

Since, f(-3) and f$\big(\dfrac{1}{2}\big)$ = 0 , hence, (x + 3) and (2x - 1) are factors of 2x² + 5x - 3.