Question

Factorise, using remainder theorem:
(1) x3 - 19x -30 (ii) x + 7x? - 21x - 27
(iii) x - 3x² - 9x - 5 (iv) 2x + 9x2 + 7x - 6​

Answer 1

If  2x + 7 in factor  of 2x3 + 5x2 – 11x – 14

then on putting  2x + 7 = 0

x = - 7/2

f(-7/2) = 0

= 2(- 7/2)3 + 5(- 7/2)2 – 11(- 7/2) – 14

= - 343/4 + 245/4 + 77/2 – 14

= - 399/4 + 245 + 154/4

= - 399 + 399/4 = 0

Hence  2x + 7 is one factor.

Now  2x3 + 5x2 – 11x – 14

= x2(2x + 7) – x(2x + 7) – 2(2x + 7)

= (2x + 7)(x2 – x – 2)

= (2x + 7)(x2 + x – 2x – 2)

= (2x + 7)[x(x + 1) – 2(x + 1)]

= (2x + 7)(x – 2)(x + 1)