Answer: the solutions of the equation are
x = - 1
x = 8
x = 9
Step-by-step explanation:
The given cubic equation is expressed as
x³ - 16x² + 55x + 72 = 0
The first step is to test for any value of x that satisfies the equation when
x³ - 16x² + 55x + 72 = 0
Assuming x = - 1, then
- 1³ - 16(-1)³ + 55(-1) + 72 = 0
- 1 - 16 - 55 + 72 = 0
0 = 0
It means that x + 1 is a factor.
To determine the other factors, we would apply the long division method. The steps are shown in the attached photo. Looking at the photo, we would factorize the quadratic equation which is expressed as
x² - 17x + 72 = 0
x² - 9x - 8x + 72 = 0
x(x - 9) - 8(x - 9) = 0
(x - 9)(x - 8) = 0
