Question

Show that 2x – 3 is a factor of x + 2x³ – 9x² + 12.

Answer 1

Let p(x) = 2x³ – 9x² + x + 12

We have to show that, 2x – 3 is a factor of p(x).

i.e., `p(3/2) = 0`

Now, `p(3/2) = 2(3/2)^3 - 9(3/2)^2 + 3/2 + 12`

= `2 xx 27/8 - 9 xx 9/4 + 3/2 + 12`

= `27/4 - 81/4 + 3/2 + 12`

= `(27 - 81 + 6 + 48)/4`

= `(81 - 81)/4` 

= 0

Hence, (2x – 3) is a factor of p(x).