Answer:
P(x) = (x +1)(x -2)(x -4)
see the 2nd attachment for a graph
Explanation:
You want the factors of P(x) = x³ - 5x² + 2x + 8, given that (x+1) is one of the factors. You also want a graph of it.
Synthetic division
The quotient from dividing P(x) by the given factor will be a quadratic we can factor to find the other two binomial factors. The first attachment shows that quotient is (x² -6x +8).
Factors
To factor this quadratic, we look for factors of 8 that have a sum of -6. They are -2 and -4. Hence the remaining binomial factors are (x -2)(x -4).
The desired product is ...
P(x) = (x +1)(x -2)(x -4)
Graph
The second attachment shows a graph of P(x). The y-intercept is the constant in the equation, 8. The x-intercepts are the values of x that make the factors zero.