1. Finding Real Roots of Polynomial Equations 3-5
Warm Up
Lesson Presentation
Lesson Quiz
Holt McDougal Algebra 2
Holt Algebra 2

2. Warm Up Factor completely. 1. 2y3 + 4y2 – 30y 2y(y – 3)(y + 5)
2. 3x4 – 6x2 – 24
3(x – 2)(x + 2)(x2 + 2)
Solve each equation.
3. x2 – 9 = 0
x = – 3, 3
4. x3 + 3x2 – 4x = 0
x = –4, 0, 1

3. Sometimes a polynomial equation has a factor that appears more than once. This creates a multiple root. In 3x5 + 18x4 + 27x3 = 0 has two multiple roots, 0 and –3. For example, the root 0 is a factor three times because 3x3 = 0.
The multiplicity of root r is the number of times that x – r is a factor of P(x). When a real root has even multiplicity, the graph of y = P(x) touches the x-axis but does not cross it. When a real root has odd multiplicity greater than 1, the graph “bends” as it crosses the x-axis.

5. Example 1A: Using Factoring to Solve Polynomial Equations
Solve the polynomial equation by factoring.
4x6 + 4x5 – 24x4 = 0

6. Example 1B: Using Factoring to Solve Polynomial Equations
Solve the polynomial equation by factoring.
x = 26x2

7. Check It Out! Example 1a
Solve the polynomial equation by factoring.
2x6 – 10x5 – 12x4 = 0

8. Check It Out! Example 1b
Solve the polynomial equation by factoring.
x3 – 2x2 – 25x = –50

9. p # 2-7, 15-19,