Question

for what value of k the polynomials 2x³-kx²+5x+9 is divided by 2x+3 ​

Answer 1

Since the polynomial 2x+3 is a factor of 2x³-kx²+5x+9

Zero of the polynomial

2x+3 = 0

2x = -3

x= -3/2

$2 \: \frac{ { - 3}^{3} }{2} - k \frac{ { - 3}^{2} }{2} + 5 \frac{ - 3}{2} + 9 \\ \\ 2 \frac{ - 27}{8} - k \frac{9}{4} + 5 \frac{ - 3}{2} + 9$