Warm Up Feb. 19 th

1. Warm Up Feb. 19th • 1. Solve x4 – 6x2 = 27 • 2. State the zeros of x(x + 2)(3x – 7)2 • 3. Write a polynomial in standard form with zeros at 0, 2 and 3i.

2. Homework Questions??

3. Finding All Zeros of Any Polynomial Long & Synthetic Division

4. 4th Grade Review – No Calc. 1. 1424 ÷ 8 2. 9706 ÷ 4

5. Long Division • Divide x2 – 5x – 24 by x + 3.

6. (9b2 + 9b – 10) ÷ (3b – 2)

7. (6x3 + 2x2 – 11x – 12) ÷ (3x + 4)

8. Synthetic Division • Rules: Divisor must be a linear binomial with a leading coefficient of 1. (x + 4) or (x – 9) • Dividend must be in standard form with “place holders” for missing terms

9. Examples • (2x3 – 7x2 – 8x + 16) ÷ (x – 4)

11. Examples

12. Remainder Theorem Is (x – 3) a factor of 6x3 – 19x2 + x + 6?

13. Remainder Theorem Given: f(x)=x4 – 16x3 – 37x2 + 18x + 13. Evaluate f(18) without a calculator.

14. Warm Up Feb. 20th • 1. The volume of a rectangular prism is given by • V(x) = x3 + 3x2 – 36x + 32. The length is given by x – 4. Find the missing measures. • 2. Find the value of k so that the remainder is 3 for • (x2 + 5x + 7) ÷ (x + k)

15. Homework Answers & Questions

16. Finding All Zeros • For f(x) = 2x3 + x2 + 1, x = -1 is a zero. Find the others.

17. For f(x) = x4 – 3x2 – 4, x = 2 and x = -2 are zeros. Find the others.

18. Rational Root Theorem • Find all zeros for x3 – 5x2 + 5x – 4.

19. Find all zeros for x4 – 20x2 + 24x – 5.

20. Test Review • Topics: • Solving Quadratics, Radicals and Complex Numbers from Last Unit • Polynomials Graphs – end behavior, domain and range, extrema (max and mins), zeros, increasing/decreasing, regression (best fit model) applications and optimization word problems • KNOW YOUR CALC. STEPS!! • Writing Polynomials – turning zeros into factors and multiply • Solving Polynomials – by factoring (perfect cubes and special quartics), long/synthetic division, remainder theorem, rational root theorem