Section 5.3 – Solving Polynomial Equations

Students will be able to:•Solve polynomial equations by factoring•Solve polynomial equations by graphing

Lesson Vocabulary•Sum of Cubes

•Difference of Cubes

Section 5.3 – Solving Polynomial Equations

To solve a polynomial equations by factoring:1. Write the equation in the form P(x) = 0 for

some polynomial function P.2. Factor P(x). Use the Zero Product Property to

find the roots.

Section 5.3 – Solving Polynomial EquationsProblem 1:

What are the real or imaginary solutions of each polynomial equation?

2x3 – 5x2 = 3x

Section 5.3 – Solving Polynomial EquationsProblem 1b:

What are the real or imaginary solutions of each polynomial equation?

3x4 + 12x2 = 6x3

Section 5.3 – Solving Polynomial EquationsProblem 1c:

What are the real or imaginary solutions of each polynomial equation?

(x2 – 1)(x2 + 4) = 0

Section 5.3 – Solving Polynomial EquationsProblem 1d:

What are the real or imaginary solutions of each polynomial equation?

x5 + 4x3 = 5x4 – 2x3

Section 5.3 – Solving Polynomial Equations

Section 5.3 – Solving Polynomial Equations

Section 5.3 – Solving Polynomial Equations

Section 5.3 – Solving Polynomial EquationsProblem 2:

What are the real or imaginary solutions of each polynomial equation?

x4 – 3x2 = 4

Section 5.3 – Solving Polynomial EquationsProblem 2b:

What are the real or imaginary solutions of each polynomial equation?

x3 = 1

Section 5.3 – Solving Polynomial EquationsProblem 2c:

What are the real or imaginary solutions of each polynomial equation?

x4 = 16

Section 5.3 – Solving Polynomial EquationsProblem 2c:

What are the real or imaginary solutions of each polynomial equation?

x3 = 8x – 2x2

Section 5.3 – Solving Polynomial EquationsProblem 2d:

What are the real or imaginary solutions of each polynomial equation?

x(x2 + 8) = 8(x +1)

Section 5.3 – Solving Polynomial Equations

While factoring is an effective way to solve a polynomial equation, you can also find the

REAL roots quickly by using a graphing calculator.

Problem 3:What are the real solutions of the equation

x3 + 5 = 4x2 + x?

Section 5.3 – Solving Polynomial EquationsProblem 3b:

What are the real solutions of the equationx3 + x2 = x – 1?

Section 5.3 – Solving Polynomial EquationsProblem 4:

Close friends Stacy, Una, and Amir were all born on July 4. Stacy is one year younger than

Una. Una is 2 years younger than Amir. On July 4, 2010, the product of their ages was

2300 more than the sum of their ages. How old was each friend on that day?

Section 5.3 – Solving Polynomial EquationsProblem 5:

The width of a box is 2 m less than the length. The height is 1 m less than the length. The volume is 60 cubic m. What is the length of

the box?

Section 5.3 – Solving Polynomial EquationsProblem 6:

The product of three consecutive integers is 210. What are the numbers?

Section 5.3 – Solving Polynomial EquationsProblem 7:

A student claims that 1, 2, 3, and 4 are all zeros of a cubic polynomial function. Explain why

the student must be mistaken.