Show that (x - 2) is a factor 3x² - x - 10. Hence, factorize 3x² - x - 10.

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

f(x) = 3x² - x - 10

(x - 2) is a factor of f(x), if f(2) = 0

f(2) = 3(2)² - 2 - 10

= 12 - 12 = 0

Hence, x - 2 is a factor of 3x² - x - 10.

Now, factorizing $3x^2 - x - 10$,

$\Rightarrow 3x^2 - 6x + 5x - 10 \\[0.5em] \Rightarrow 3x(x - 2) + 5(x - 2) \\[0.5em] \Rightarrow (3x + 5)(x - 2)$

Hence, 3x² - x - 10 = (x - 2)(3x + 5).