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Name _______________________________________ Date __________________ Class __________________ Unit 2 Final Review Polynomials 1. Rewrite the polynomial in standard form. Then identify the leading coefficient, degree, and number of terms. Name/classify the polynomial. x 2 3 2x 5 7x 4 12x ________________________________________________________________________________________ 2. Find h(x) – 4k(x) for h(x) = x2 – 8 and k(x) = 3x3 – 6x – 4 + 9x2 ________________________________________________ _ 3. Find the product: (x 2)(x 2 2x 12) ______________________________________________________ 4. Use the Binomial Theorem to expand the binomial: (2x 7)4 ______________________________________________________ 5. Divide by using long division: (2x 3 10x 2 x 5) (x 5) ______________________________________________________ 6. Divide by using synthetic division: (3x 2 8x 4) (x 2) ______________________________________________________ 7. Write the expression that represents the length of a rectangle with width x + 3 and area 5x2 – 4x + 12. ______________________________________________________ 8. Solve the polynomial equation by factoring: x 5 2x 4 24x 3 0 ______________________________________________________ Name _______________________________________ Date __________________ Class __________________ 9. Use the graph of f(x) = x 4 2x 3 8x 2 0 to identify the values of x for which f(x) = 0 and to factor f(x). 10. Identify the roots of the equation. State the multiplicity of each root. x 3 5x 2 8x 48 0 ______________________________________________________ 11. Solve the equation by finding all roots: x 4 2x 3 14x 2 2x 15 0 ______________________________________________________ 12. Factor: x 3 3x 2 9x 27 0 ______________________________________________________ 13. Write the polynomial function that has zeros at 5 and 2 - i. ______________________________________________________ 14. Identify the leading coefficient, degree, and end behavior: Q(x) 4x 3 x 1 ______________________________________________________ Name _______________________________________ Date __________________ Class __________________ 15. Identify whether the function graphed has an odd or even degree and a positive or negative leading coefficient. _____________________________________ 16. Graph the function P(x) x 3 6x 2 5x 12. 17. Find the first 5 terms of the sequence: an n2 2n ______________________________________________________ 18. Find the 8th term of the geometric sequence with the given terms: a11 4 and a13 36 ______________________________________________________ Find the indicated sum for each geometric series. 19. S7 for 14, 42, 126, 378, 8 20. 4 k 1 k 1 _______________________ _____________________