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CCGPS Advanced Algebra Name____________________________________ Unit: 2 Unit 2: Polynomial Functions Date_____________________ Homework: 10 Standard: Use complex numbers in polynomial identities and equations. MCC9‐12.N.CN.8 (+) Extend polynomial identities to the complex numbers. Interpret the structure of expressions. MCC9‐12.A.SSE.1a Interpret parts of an expression, such as terms, factors, and coefficients. ★ MCC9‐12.A.SSE.1bInterpret complicated expressions by viewing one or more of their parts as a single entity★ MCC9‐12.A.SSE.2 Use the structure of an expression to identify ways to rewrite it. Use polynomial identities to solve problems. MCC9‐12.A.APR.4 Prove polynomial identities and use them to describe numerical relationships. MCC9‐12.A.APR.5 (+) Know and apply that the Binomial Theorem gives the expansion of (x + y) n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle. (The Binomial Theorem can be proved by mathematical induction or by a combinatorial argument.) Essential Question: How do polynomial identities help when expanding or factoring polynomials? How can multiplication of binomials be used to find products of complex numbers? What patterns are used to find powers of binomials? Key Words: Binomial Theorem, complex conjugate, complex number, factorial, imaginary number, imaginary unit, I, Pascal’s Triangle, polynomial identity, sigma (uppercase), Σ Recommended Resources: http://www.walch.com/rr/00161 http://www.walch.com/rr/00162 http://www.walch.com/rr/00163 http://www.walch.com/rr/00164 Use polynomial identities to expand or factor each expression. 1. (x – 16)2 2. (4x + 21)2 3. 100x2 – 4 4. x2 – 81 5. 27c3 + 343 6. 512x3 - 8 7. (x2 + x + 3) 2 Find the area of a square with the given side length, without using a calculator. The area of a square is the square of the side length, or area = side2. 8. side length = 530 feet 9. side length = 470 meters 10. side length = 310 centimeters Use properties of complex numbers to expand or factor each expression. 11. (20 + i)(20 – i) 12. (4 + 3i)(4 – 3i) 13. (7x + i)(7x – i) 13. x2 + 64 14. 25x2 + 484 15. (9x + 15i)(9x – 15i) 16. 36x2 + 144 Find the coefficient of the given term in the specified row of Pascal’s Triangle. 17. row 4, term 1 18. row 10, term 3 Expand each binomial using the Binomial Theorem. 19. (–8x + 4)3 20. (2x + y)5 Find the given term in the expanded form of each binomial. 21. (4x + 1)6, term 4 23. (3x + y)10, term 8 22. (2x – 3y)5, term 3