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Home > INT3 > Chapter 8 > Lesson 8.3.2 > Problem 8-121

8-121.
  1. Given the polynomial p(x) = x3 – 6x2 + 7x + 2: Homework Help ✎

    1. Use the Remainder Theorem to determine p(2).

    2. Now use the Factor Theorem to determine one factor of x3 – 6x2 + 7x + 2. (See the Math Notes box in this lesson.)

    3. Use your answer to part (b) to determine another factor.

    4. 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.