2x - 3
2x - 3 (4x² + bx + 9
- (4x² - 6x)
(b + 6)x + 9
- (-6x + 9)
(b + 6)x - (-6x) = 0 it must equal zero if 2x - 3 is a factor
bx + 6x + 6x = 0
bx + 12x = 0
bx = -12x
b = -12
Answer: b = -12
You can check by multiplying (2x - 3) the factor given and (2x - 3) the factor found when dividing by the given factor.
(2x - 3)(2x - 3) = 4x² -12x + 9
