Find the value of b so that 4x^2+bx+9 has a factor of 2x-3

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