6.2 Review Worksheet, Part 1
6.2.1 Finding Real Roots of Polynomial Equations Solve each polynomial equation by factoring. 1. x 3 + 3 x 2 − 9 x = 27 2. 4 x 5 − 8 x 3 + 4 x = 0
3. 10 x 3 − 640 x = 0
4. x 4 − 12 x 2 = − 36
5. 2 x 3 − 5 x 2 − 4 x + 10 = 0
6. 4 x 3 + 7 x 2 − 5 x = 6
Identify the roots of each equation. State the multiplicity of each root. 7. 8 x 5 − 192 x 4 + 1536 x 3 − 4096 x 2 = 0
8. x 4 + 2 x 3 − 11 x 2 − 12 x + 36 = 0
9. An open box is to be made from a square piece of material with a side length of 10 inches by cutting equal squares from the corners and turning up the sides. What size of square would you cut out if the volume of the box must be 48 cubic inches?
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x
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Identify all of the real roots of each equation. 10. x 4 − 3 x 2 − 4 = 0
11. 3 x 3 + 4 x 2 − 6 x − 8 = 0
12. x 4 − 2 x 3 − 2 x 2 = 0
6.2.2 Fundamental Theorem of Algebra Write the simplest polynomial function with the given zeros. 13. − 1, − 1, 2 14. 2,1,
2 3
15. − 4, − 1, 2
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