Question

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

 p(x) = 2x³ – x² – 45 ; q(x) = x – 3

Answer 1

p(x) = 2x³ – x – 45 

Divisor = q(x) = x – 3 

take x = 3 

Remainder = p(3) 

p(x) = 2x³ – x²– 45 

P(3) = 2(3)³ – (3)² – 45 

= 2(27) – 9 – 45 

= 54 – 9 – 45

 = 0

 ∴ By factor theorem, x – 3 is a factor of 2x³ – x² – 45.