Question

4. P(x) = x³ - 5x² + 2x + 8. We know (x + 1)is a factor of P(x). Find the other two

factors then write P(x) as a product of three linear factors and sketch the graph of P(x).

Answer 1

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.