6.2.1 Finding Real Roots of Polynomial Equations - Worksheet
Example 1: Solve each polynomial equation by factoring. 1. 2 x 4 + 16 x 3 + 32 x 2 = 0
2. x 4 − 37 x 2 + 36 = 0
3. 4 x 7 − 28 x 6 = − 48 x 5
4. 3 x 4 + 11 x 3 = 4 x 2
5. 2 x 3 − 12 x 2 = 32 x − 192
6. x 4 + 100 = 29 x 2
Example 2: Identify the roots of each equation. State the multiplicity of each root. 7. 2 x ( x + 1 )( x − 1)( x + 3)( x + 3) = 0
8. ( x + 2)( x − 2)( x + 2)( x − 2)( x + 2)( x − 2) = 0
Example 3: 9. A cedar chest has a length that is 3 feet longer than its width and a height that is 1 foot longer than its width. The volume of the chest is 30 cubic feet. What is the width?
Example 4: Identify all of the real roots of each equation. 10. x 3 + 6 x 2 − 5 x − 30 = 0
11. 3 x 3 − 18 x 2 − 9 x + 132 = 0
12. 2 x 3 − 42 x + 40 = 0
13. x 4 − 9 x 2 + 20 = 0
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