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# 5.3

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### 5.3

1. 1. 5.3 Solving PolynomialEquations
2. 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. 3. To Solve a Polynomial Equationby Factoring:1. Set the equation = 02. 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. 4. Example: Find the real orimaginary solutions of eachequation.
5. 5. Example: Find the real orimaginary solutions of eachequation.
6. 6. Factoring a Sum or Difference ofCubes To factor a sum or difference of cubes, we use the following “shortcut”
7. 7. Example: Factor
8. 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. 9. Solving by Factoring withSubstitution1. Write the polynomial in standard form2. Identify the piece that will be substituted3. Substitute4. Factor5. Undo the substitution6. Solve for the variable
10. 10. Find the real or imaginarysolutions of each equation byfactoring.
11. 11. Find the real or imaginarysolutions of each equation byfactoring.
12. 12. Finding Real Roots byGraphing1. Write the equation in standard form2. Enter the equation into3. Use the zero feature to find all real zerosExample: Find the Real Solutions of the equation by graphing.
13. 13. Assignment Classwork: p 301 #25 – 29 odd Homework: p 301 #11 – 23odd, 39 – 49odd, not 45