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

8-121.

Given the polynomial

*p*(*x*) =*x*^{3}– 6*x*^{2}+ 7*x*+ 2: Homework Help ✎Use the Remainder Theorem to determine

*p*(2).Now use the Factor Theorem to determine one factor of

*x*^{3}– 6*x*^{2}+ 7*x*+ 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

*x*^{3}– 6*x*^{2}+ 7*x*+ 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.

(*x*^{2} − 4*x* − 1)

See part (a) for one solution.

Use the Quadratic Formula to find the solutions to

0 = *x*^{2} − 4*x* − 1.