Question

Using the Reminder Theorem, factorise each of the following completely.

(i)  3x³ + 2x² - 19x + 6

(ii)2x³ + x² – 13x + 6

(iii) 3x³ + 2x² – 23x – 30

(iv) 4x³ + 7x² – 36x − 63

(v) x³ + x² – 4x – 4

Answer 1

(ii) Let f (x) = 2x³ + x² − 13x + 6

For x = 2,

f(x) = f(2) = 2(2)³ + (2)² − 13(2) + 6 = 16 + 4 − 26 + 6 = 0

Hence, (x − 2) is a factor of f(x).