This document discusses solving polynomial equations by factoring. It provides examples of factoring polynomials, including factoring the difference and sum of cubes. Factoring by substitution is also introduced as a method for factoring polynomials of degree 4 or higher. The document demonstrates solving polynomial equations by factoring the expressions and setting each factor equal to 0. Both real and imaginary solutions may be obtained depending on whether the factors are real or complex numbers. Graphing is presented as an alternative method to find real solutions of a polynomial equation.

1. 5.3 Solving Polynomial
Equations

2. Real Vs. Imaginary
 In Chapter 4, we found both real and
imaginary solutions for quadratic
equations.
 We can find both real and imaginary
solutions for polynomial equations too!
◦ Remember:

3. To Solve a Polynomial Equation
by Factoring:
1. Set the equation = 0
2. Factor (Remember GCF first!)
3. Apply the Zero-Product Property
(Set each factor = 0 and solve for x)
 If you have a quadratic that is not
factorable, use the quadratic formula

4. Example: Find the real or
imaginary solutions of each
equation.

5. Example: Find the real or
imaginary solutions of each
equation.

6. Factoring a Sum or Difference of
Cubes
 To factor a sum or difference of cubes,
we use the following “shortcut”

7. Example: Factor

8. Factoring by Substitution
 Factoring by substitution is useful
when you have a polynomial of degree
4 or higher and no GCF
 It is also useful if you have a variable
in the denominator (more about this
later!)

9. Solving by Factoring with
Substitution
1. Write the polynomial in standard form
2. Identify the piece that will be
substituted
3. Substitute
4. Factor
5. Undo the substitution
6. Solve for the variable

10. Find the real or imaginary
solutions of each equation by
factoring.

11. Find the real or imaginary
solutions of each equation by
factoring.

12. Finding Real Roots by
Graphing
1. Write the equation in standard form
2. Enter the equation into
3. Use the zero feature to find all real
zeros
Example: Find the Real Solutions of the
equation by graphing.

13. Assignment
 Classwork: p 301 #25 – 29 odd
 Homework: p 301 #11 – 23odd, 39 –
49odd, not 45