Given the polynomial p(x) = x3 – 6x2 + 7x + 2: Homework Help ✎
Use the Remainder Theorem to determine p(2).
Now use the Factor Theorem to determine one factor of x3 – 6x2 + 7x + 2. (See the Math Notes box in this lesson.)
Use your answer to part (b) to determine another factor.
What are all the solutions of x3 – 6x2 + 7x + 2 = 0?
Divide the polynomial by (x − 2). What is the remainder?
Since p(2) = 0, x = 2 is the zero of the function. What is the corresponding factor?
(x − 2)
Try using an area model.
(x2 − 4x − 1)
See part (a) for one solution.
Use the Quadratic Formula to find the solutions to
0 = x2 − 4x − 1.