1. Consider f(x) = -8x 2 + 3x 4 + 5 – 2x 1. Write the polynomial function in standard form, then give the degree, leading coefficient, constant term, and its name. 2. Use direct substitution to evaluate f(x) if x = -3. 3. Evaluate f(-1)? 4. What is the end behavior for the polynomial function? 5. Graph the polynomial function. Algebra II 1

2. Adding, Subtracting, and Multiplying Polynomials Algebra II

3. 1. a m · a n = a m+n 2. a m = a m-n 3. (a m ) n = a m·n 4. (ab) m = a m b m 5. (a/b) m = a m /b m 6. a -m = 1 7. a 0 = 1 anan amam Algebra II 3 Product Property Quotient Property Power Property Power of a Product Power of a Quotient Negative Exponent Zero Exponent

4. It is common practice to write our answers using POSTIVE exponents ONLY! **(unless otherwise stated)** 4 Algebra II

5. 1. 2. 3. 5 Algebra II 4. 5. 6.

6. Perform the indicated operations. 1. (-4x 2 – 6x +18) + (-x 2 + 7x + 8) -5x 2 + x + 26 2. (6x 2 – 12x+ 48) – (-x 2 + 24x – 63) 6x 2 – 12x + 48 + x 2 – 24x + 63 7x 2 – 36x + 111 Algebra II 6

7. Perform the indicated operations. 3. Subtract -11x 4 + 5x 2 – 7x + 13 from –11x 4 – x 3 – 3x 2 + 10x – 2 (–11x 4 – x 3 – 3x 2 + 10x – 2) – ( -11x 4 + 5x 2 – 7x + 13) –11x 4 – x 3 – 3x 2 + 10x – 2 + 11x 4 – 5x 2 + 7x – 13 -x 3 – 8x 2 + 17x - 15 Algebra II 7

8. Perform the indicated operation. 4. 2x 2 (2x 3 – x 2 + 3x – 5) 4x 5 – 2x 4 + 6x 3 – 10x 2 5. (x 4 – 10x 2 + 25)(3x 2 – 6x – 1) 3x 6 – 6x 5 – x 4 – 30x 4 + 60x 3 + 10x 2 + 75x 2 – 150x – 25 3x 6 – 6x 5 – 31x 4 + 60x 3 + 85x 2 – 150x – 25 Algebra II 8

9. Perform the indicated operation. 6. (x + 1)(x – 2)(x + 6) (x 2 – x – 2)(x + 6) x 3 + 6x 2 – x 2 – 6x – 2x – 12 x 3 + 5x 2 – 8x – 12 7. (2x – 3)(6 – x)(4 – 5x) (12x – 2x 2 – 18 + 3x)(4 – 5x) (15x – 18 – 2x 2 )(4 – 5x) 60x – 75x 2 – 72 + 90x – 8x 2 + 10x 3 10x 3 – 83x 2 + 150x – 72 Algebra II 9

10. Perform the indicated operation. 8. (3y – 8)(3y + 8) 9y 2 + 24y – 24y – 64 9y 2 – 64 9. (2v – 1) 3 (2v – 1)(2v – 1)(2v – ) (4v 2 – 4v + 1)(2v – 1) 8v 3 – 4v 2 – 8v 2 + 4v + 2v – 1 8v 3 – 12v 2 + 6v – 1 Algebra II 10

11. Perform the indicated operation. Extra: (2m + 3) 2 (2m + 3)(2m + 3) 4m 2 + 12m + 9 Extra: (3m – 5) 3 (3m – 5)(3m – 5)(3m – 5) (9m 2 – 30m + 25)(3m – 5) 27m 3 – 45m 2 – 90m 2 + 150m + 75m – 125 27m 3 – 135m 2 + 225m – 125 Algebra II 11

12.  This shows the pattern of how to raise a binomial to a power 12 Algebra II

13.  Ex: (x – 2) 4  Ex: (2x + 3) 3 13 Algebra II

14. 11. Find the Volume: 4x – 3 2x + 1 x – 2 V= (l)(w)(h) V = (4x – 3)(2x + 1)(x – 2) V = (8x 2 – 2x – 3)(x – 2) V = 8x 3 – 18x 2 + x + 6 Algebra II 14

15. 12. Find the volume in terms of x if the radius is 4x and the height is 2x – 3. 15 Algebra II