Algebra T3 – Lesson 10.1

1. Daily Warm-Up Simplify. Combine Like Terms. 4y – 2x + 4 – 3y – (-3) + 8y + (-7x) Tonight’s Homework P. 580 #’s 14-54 EVEN + PREVIEW L 10.2 Algebra T3 – Lesson 10.1

2. 10.1 Adding and Subtracting Polynomials Objectives: Know the anatomy of a polynomial Add and subtract polynomials Algebra T3

3. Vocabulary – PAGE 576 Polynomial Standard form Degree Degree of polynomial Leading Coefficient Term Monomial Binomial Trinomial

4. Term vs. Coefficient Term Coefficient -12x³ ? x³y ? -z ? 2 ? Constant – If a term contains only a number like 2 it is called a constant.

5. Types of Polynomials All other longer polynomials do not have a special name.

6. There are two ways to classify polynomials: • degree – find the largest degree • number of terms – count the number of terms • SEE EXAMPLE 2 on Page 576

7. Polynomial Classifications

8. Polynomial in standard form 2x³ + 5x² - 4x + 7 Degree of each term – sum of the exponents of the variables. Degree of 2x³y²z is (3+2+1)=6 Degree of polynomial – largest degree of any of its terms. Leading Coefficient Degree Constant Term

9. Anatomy of a Polynomial terms degree constant degree of polynomial standard form leading coefficient

10. Anatomy of a Polynomial terms degree constant degree of polynomial standard form leading coefficient

11. Anatomy of a Polynomial terms degree constant degree of polynomial standard form leading coefficient

12. Anatomy of a Polynomial terms degree constant degree of polynomial standard form leading coefficient

13. Like Terms: terms that have identical variables both in letters and degree Combining Like Terms: adding and subtracting like terms – changes only the coefficient • Adding and Subtracting Polynomials: simply combining like terms • 2 ways to add and subtract • Horizontal • Vertical

14. Adding & Subtracting Horizontally (6x2 – x + 3) + (-2x + x2 – 7) • Steps: • Distribute all subtraction signs into polynomials. • Combine like terms

15. Adding & Subtracting Horizontally (6x2 – x + 3) – (-2x + x2 – 7) • Steps: • Distribute all subtraction signs into polynomials. • Combine like terms

16. Take a 5 Minute Brain Break

17. Adding & Subtracting Horizontally (-6x3 + 5x – 3) – (2x3 + 4x2 – 3x + 1) • Steps: • Distribute all subtraction signs into polynomials. • Combine like terms

18. Adding & Subtracting Horizontally (-8x3 + x – 9x2 + 2) + (8x2 – 2x + 4) + (4x2 – 1 – 3x3) • Steps: • Distribute all subtraction signs into polynomials. • Combine like terms

19. Adding & Subtracting Vertically (-6x3 + 5x – 3) – (2x3 + 4x2 – 3x + 1) • Steps: • Put each polynomial on a level in standard form lining up like terms • Carefully add or subtract the coefficients

20. Adding & Subtracting Vertically (4x2 – 1) – (3x – 2x2) • Steps: • Put each polynomial on a level in standard form lining up like terms • Carefully add or subtract the coefficients

21. Adding & Subtracting Vertically (-8x3 + x – 9x2 + 2) + (8x2 – 2x + 4) – (4x2 – 1 – 3x3) • Steps: • Put each polynomial on a level in standard form lining up like terms • Carefully add or subtract the coefficients

22. Find the sum or difference: (2x2 + 9x – 4) + (6x – 3x2 + 1) – (x2 + x + 1) • Steps: • Put each polynomial on a level in standard form lining up like terms • Carefully add or subtract the coefficients

23. DAILY HOMEWORK QUIZ Find the Difference. (x³ - 3x + 6) – (4 – 4x² + 3x³) Tonight’s Homework P. 580 #’s 14-54 EVEN + PREVIEW L 10.2 Algebra T3 – Lesson 10.1