Question

  Factorise 2x³ – x² – 12x – 9 into linear factors.

Answer 1

Let p(x) = 2x³ – x² – 12x – 9

Sum of the co-efficients = 2 – 1 – 12 – 9 = -20 ≠ 0 

Hence x – 1 is not a factor 

Sum of co-efficients of even powers with constant = -1 – 9 = -10 

Sum of co-efficients of odd powers = 2 – 12 = -10 

Hence x + 1 is a factor of x. 

Now we use synthetic division to find the other factors.

Then p(x) = (x + 1)(2x² – 3x – 9)

Now 2x² – 3x – 9 = 2x² – 6x + 3x – 9 = 2x(x – 3) + 3(x – 3)

= (x – 3)(2x + 3)

Hence 2x³ – x² – 12x – 9 = (x + 1) (x – 3) (2x + 3)