1. 10/20/2015 12:04 AMR-4 - Polynomials1 WARM-UP Simplify: – 1. 2. Determine the area and circumference of a circle where the radius is 8 cm. Determine the length of a rectangle in which the area is 20 cm and the width is 5 cm.

2. 10/20/2015 12:04 AMR-4 - Polynomials2 Section R-4 P O L Y N O M I A L S

3. 10/20/2015 12:04 AMR-4 - Polynomials3 REVIEW Coefficient: The number in front of the variable. Degree: The sum of the exponents of the variables. ADD THE TOTAL EXPONENTS Term: Parts of an expression that is added or subtracted Constant Term: The number at the end of the equation that doesn’t have the variable. Standard Form: Descending degree form in equation.

4. 10/20/2015 12:04 AMR-4 - Polynomials4 CLASSIFYING POLYNOMIALS Refresh: Standard Form: Descending degree form in equation. Rewrite each polynomial in standard form. 2. 5x 2 – 4 + 8x 4 + x 8x 4 + 5x 2 + x – 4 Write terms in descending order by degree.

5. 10/20/2015 12:04 AMR-4 - Polynomials5 EXAMPLE 1 Add (x + 2) + (x + 3) and express answer as a single polynomial in standard form: 2x + 5

6. 10/20/2015 12:04 AMR-4 - Polynomials6 EXAMPLE 2 Subtract (x + 2) – (x – 3) and express answer as a single polynomial in standard form: 5

7. 10/20/2015 12:04 AMR-4 - Polynomials7 EXAMPLE 3 Simplify x + 2 – x – 3 and express answer as a single polynomial in standard form: – 1

8. 10/20/2015 12:04 AMR-4 - Polynomials8 EXAMPLE 4 Simplify (8x 3 – 2x 2 + 6x – 2) + (3x 4 – 2x 3 + x 2 + x) and express answer as a single polynomial in standard form: 3x 4 + 6x 3 – x 2 + 7x – 2

9. 10/20/2015 12:04 AMR-4 - Polynomials9 YOUR TURN Simplify (8x 3 – 2x 2 + 6x – 2) – (3x 4 – 2x 3 + x 2 + x) and express answer as a single polynomial in standard form: 5x 4 + 10x 3 – 3x 2 + 5x – 2

10. 10/20/2015 12:04 AMR-4 - Polynomials10 MULTIPLYING POLYNOMIALS First Outer Inner Last Box Method

11. 10/20/2015 12:04 AM5.1 Multiplying Factors11 MULTIPLYING POLYNOMIALS Using FOIL: Draw Arrows Make sure each factor is multiplied at least once Must be written in Standard Form

12. 10/20/2015 12:04 AMR-4 - Polynomials12 EXAMPLE 1 Multiply (x + 2) (x + 3) and express answer as a single polynomial in standard form.

13. 10/20/2015 12:04 AMR-4 - Polynomials13 EXAMPLE 1 Multiply (x + 2) (x + 3) and express answer as a single polynomial in standard form. x2x2 +2x +3x+6 x +3 x +2

14. 10/20/2015 12:04 AMR-4 - Polynomials14 EXAMPLE 2 Multiply (x – 5) (x + 5) and express answer as a single polynomial in standard form:

15. 10/20/2015 12:04 AMR-4 - Polynomials15 EXAMPLE 3 Simplify (x – 4) 2 and express answer as a single polynomial in standard form: NO!!!

16. 10/20/2015 12:04 AMR-4 - Polynomials16 EXAMPLE 4 Simplify (3x – 4) 2 and express answer as a single polynomial in standard form:

17. 10/20/2015 12:04 AMR-4 - Polynomials17 EXAMPLE 5 Simplify (x + 2) 3 and express answer as a single polynomial in standard form:

18. 10/20/2015 12:04 AMR-4 - Polynomials18 YOUR TURN Simplify (x – 1) 3 and express answer as a single polynomial in standard form:

19. 10/20/2015 12:04 AMR-4 - Polynomials19 ASSIGNMENT Pg 42: 27-39 odd, 41-75 every 4th