4.1 and 4.3 Practice Name: _______________________ Algebra 2 Trigonometry H – NO CALC Long Divide:

1.

3 24x +13x +27x +6

4x +1 2.

14( 8 2) 2x x x

3.

4 3 2x + x - 12x - 2x + 4

4+ x 4. Which problem(s) (#1 – 3) can you

synthetically divide? _________

5. In which problem(s) (#1 – 3) is the divisor a zero of the original polynomial ? ____ 6. What would you put “on the shelf” for

problem #1? __________ 7. What would be the factors of

3 24x +13x +27x +6 , in problem #1?

________________________________

7a. True or False: There can be more zeros

than factors? _____

Synthetically Divide:

8.

3 22x - 4x - x - 5

x +1 9.

3 22x - 5x - 1

2x - 1

Find all the zeros for each polynomial (rational, irrational, and imaginary).

10. 3 2x x 8x 12 11. 3 24x - 9x +23x +24 (calc okay)

12. 4x 8x 13. 3 22x - 3x - 8x +12

14. 4 3 215P(x) = x - 5x + x - 2x - 2

2 15. 4 3 2P(x) = x - 2x +7x -18x -18 given - 3 is one zeroi

16. What are the five properties of a polynomial, P(x) = anxn + an-1xn-1 + … + an + a0

1. 2. 3.

4. 5.

Find a polynomial that satisfies all of the given conditions. Write the polynomial using only real coefficients. 17. 2- 5i is a zero, leading coefficient 1, and degree 2 18. 7 and -2i are zeros, leading coefficient 1, and degree 3 19. 6 + i is a zero, leading coefficient 2, and degree 2 Some other problems to ponder… 20. What is the difference between a zero and an x-intercept?

21. What is the y coordinate of an ordered pair in P(x) = 3 28x x x , if the x coordinate is 0.25? 22. 23. Factor: P(x) = x3 + 3x2 + 3x + 1

24. Factor P(x) = 5 4 3 2x +2x - 6x +19x - 43x +21 , given that one factor is 3 2x - 2x +5x - 7 .

25. Determine whether the second polynomial is a factor of the first polynomial:

x33 + 3x22 - 3x11 + 1x0; x + 1