Question

Find the value of b for which 2x+3is a factor of 2x3+9x2-x-b

Answer 1

Hello Mate

Factor theorum states that p( x ) = 0

2x + 3 = 0
2x = -3
x = -3/2

p ( x ) = 2x^3 + 9x^2 - x - b
0 = 2 ( - 3/2 ) ^ 3 + 9 ( -3/2 ) ^ 2 - ( - 3/ 2 ) - b
0 = -27 / 4 + 81/4 + 3/2 - b
0 = ( - 27 + 81 + 6 ) / 4 - b
0 = 60/4 - b
0 = 15 - b
b = 15

Hope it helps☺!✌