A2T Unit Review- Polynomial Functions PDF

Unit Review: Polynomial Functions Name: _____________________________ Section 1: Polynomial Division Directions: Divide the following using long division 1. ( 3x 4 − 2 x 2 + 3 x − 1) ÷ ( x 2 + 3) 2. ( 2x 4...

Unit Review: Polynomial Functions Name: _____________________________ Section 1: Polynomial Division Directions: Divide the following using long division 1. ( 3x 4 − 2 x 2 + 3 x − 1) ÷ ( x 2 + 3) 2. ( 2x 4 − 3 x 3 + 2 x 2 + 3 x − 2 ) ÷ ( x 2 − 2 x + 1) Section 2: Applications of Synthetic Division Directions: Divide the following using synthetic division 3. (x 3 − 2 x + 5 ) ÷ ( x − 3) 4. (x 3 − 3 x 2 + 5 x − 1) ÷ ( x + 2 ) Directions: Evaluate the function P ( x ) = x 4 − 3 x 3 − 2 x + 5 using synthetic division 5. P ( 2 ) 6. P ( −1)  Unit Review: Polynomial Functions Directions: Determine if the indicated binomial is a factor of function, P ( x ) =6 x 3 + 13 x 2 − 4. If it is, factor the function completely. 7. x − 2 8. x + 2 Section II: Solving Polynomial Equations Directions: Determine the possible rational roots for the following polynomial equation. 9. 2 x3 − 3 x 2 + 2 x = 8 10. 4 x5 − 2 x3 + 3 x − 10 = 0 Directions: Determine the roots/zeros of the polynomial equation/function with the given information. 11. 6 x3 − 11x 2 − 3 x + 2 =0 ; ( x − 2 ) is a factor 12. x5 + 3 x 4 + x3 − 3 x 2 − 2 x = 0 ; x = −1 is a double root  Unit Review: Polynomial Functions  1 13. f ( x ) = 6 x3 + 29 x 2 − 7 x − 10 ; f  −  = 0  2 Directions: Determine the solutions/zeros of the polynomial equation/function. 14. 2 x 4 − 19 x 3 + 66 x 2 + 54 = 99 x 15. f ( x ) = 2 x 4 + 3 x 3 − 5 x 2 + 6 x − 18 16. x 5 − 10 x 4 + 34 x 3 − 44 x 2 + 8 x + 16 = 0  Unit Review: Polynomial Functions Section III: Practical Problems Directions: Solve the following problems. 17. A pool is being installed in your backyard. The shape of the pool is a rectangular prism. The depth of the pool is x meters , the width of the pool is 8 more than twice the depth and the length is five times the depth. If the volume of the pool is 3600 m3 , then what is the depth of the pool? 18. The profit, P (in millions of dollars) for a manufacturer of Tacky Thingamabobs can be modeled by the function, P ( x ) =− x 4 + 7 x3 − 12 x 2 − 4 x + 38 where x is the number of Tacky Thingamabobs produced (in millions). Currently, the company produces 4 million widgets and makes a profit of $22,000,000. What lesser number of widgets could the company produce and still make the same profit?  Unit Review: Polynomial Functions Section IV: Graphing Polynomials Directions: Sketch the graph each of the following polynomials and provide the requested information. 1 19. f ( x ) = − ( x − 2) ( x + 4) 2 4 Zeros and multiplicity End Behavior Extrema: Type and interval for location 20. f ( x ) = x 6 − x5 − 2 x 4 + 2 x3 + x 2 − x Zeros and multiplicity End Behavior Extrema: Type and interval for location  Unit Review: Polynomial Functions Section V: Writing Rules for Polynomial Functions Directions: Using the given information, write the rule for the polynomial function in the indicated form. 21. Find the polynomial function of least degree in standard form given zeros of 3 and − 1 − 3i 22. Find the polynomial function of least degree in standard form given zeros of -5 and − 1 + 2 3 23. Write the function graphed below in factored form. 24. Write the function that has the given the points in factored form. ( −2, 0 ) , (−5, 0), (1, 0), (0, 0), (−4, −5)  Unit Review: Polynomial Functions Section VI: Interpreting Graphs Directions: Use the graph below to provide the information requested. 25. Factors and their multiplicity Degree (circle) Leading Coefficient (circle) Odd or Even Positive or Negative End Behavior 26. Factors and their multiplicity Degree (circle) Leading Coefficient (circle) Odd or Even Positive or Negative End Behavior