Question

By using factor theorem in the following example, determine whether q(x) is a factor p(x) or not.

p(x) = 2x³ − x² − 45, q(x) = x − 3

Answer 1

p(x) = 2x³ − x² − 45

Divisor = q(x) = x − 3

∴ Let x = 3

∴ p(3) = 2 × (3)³ − (3)² − 45

= 2 × 27 − 9 − 45

= 54 − 54

= 0

So, by factor theorem q(x) = x − 3 is a factor of polynomial p(x) = 2x³ − x² − 45.