Answer:
They are -1, 4 and 7.
Step-by-step explanation:
x^3 - 10x^2 + 17x + 28 = 0
Observation of this equation shows that there is an x -intercept at x = -1 because
-1^3 - 10^(-1)^2 - 17(1) + 28 = -28 + 28
= 0.
So x + 1 must be a factor so we can do the division:
x + 1 ) x^3 - 10x^2 + 17x + 28 ( x^2 - 11x + 28
x^3 + x^2
-11x^2 + 17x
-11x^2 - 11x
28x^2 + 28
x^2 - 11x + 28 = ( x - 4)(x - 7)
x = 4, 7.
