Write Each Polynomial In Standard Form

Name______Date______Period______

Algebra 2 – Test Chapter 6

Write each polynomial in standard form. Then classify it by degree and number of terms. 1. 9x 2  2x  3x 2 Standard Form ______2. 4x(x  5)(x  6) Standard Form ______

Degree ______Degree ______

Terms ______Terms ______

3. x 1 10 20 30 Y 91 95 260 365 a. Find a cubic function to model the data.

b. Find y when x is 4

Solve each equation by graphing. Where necessary, round to the nearest hundredth. 4. y  x3  3x 2  x  3  0 5.  x3  3x  4  0 6. x 2  6x 1  0

zeros: ______zeros: ______zeros: ______

Write a polynomial function with rational coefficients in Standard Form with the given zeros. 7. 2, 3, 5 8. -1, -1, 1

For each function, determine the zeros and their multiplicity. 9. y  (x 1) 2 (2x  3)3 10. y  4x 2 (x  2)3 (x 1) Name______Date______Period______Solve each equation. (Find the Zeros by Factoring) 11. (x 1)(x 2  5x  6)  0 12. x3 10x 2 16x  0

Divide using long division. 13. (2x3 13x 2 17x 10)  (x  5) 14. (x 3  9x 2  26x  24)  (x  4)

Divide using synthetic division. 15. (x 3  4x 2  x  5)  (x  2) 16. (2x3  4x  3)  (x 1)

17. Use synthetic division and the Remainder Theorem to find P(-5) if P(x)  x 3  4x 2  x  2 Name______Date______Period______Use the Rational Root Theorem to list all possible rational roots for each equation. Which Possible Solutions Work.? 18. x3  2x 2  3x  6  0 19. x3  3x 2  x  3  0

20. Factor the expression using the sum of cubes. x3 + 64

21. Factor the expression using the difference of cubes. Then solve to find all the complex roots.

x3 – 125 = 0