Question

Is 2x - 3 is a factor of 9x3 - 12x2 - 3x + 6? Justify your answer.

Answer 1

Using Remainder theorem

2x-3=0

2x=3

x= 3/2

f(x) = 9x³ - 12x² - 3x + 6

f(3/2)= 9(3/2)³-12(3/2)²-3(3/2)+6

$\: \: \: \: \: \: \: \: \: \: = \frac{243}{8} - \frac{108}{4} - \frac{ 9}{2} + 6 \\ \: \: \: \: \: \: \: \: \: \: = \frac{243 - 216 - 36 + 48}{8} \\ \: \: \: \: \: \: \: \: \: = \frac{39}{8}$

Remainder = 39/8

Therefore,

2x - 3 is not a factor of 9x³ - 12x² - 3x + 6