1. ADDITION AND SUBTRACTION OF POLYNOMIALS CHAPTER 4 SECTION 4 MTH 10905 Algebra

2. Polynomial (“poly” means many) Polynomial in x is an expression containing the sum of a finite number of terms of the form ax n, any real number a and any whole number n Polynomial are expressions not equations. Expressions is a collection of numbers, letters, grouping symbols, and operations. Equation shows that two expressions are equal. Examples: 2xx 2 – 2x + 1

3. Polynomial Answers should be in descending order (or descending powers) of the variable unless otherwise instructed. 2x 4 + 4x 2 - 6x + 3 Monomial is a Polynomial with one term. Example: 8 because 8x 0 4x because 4x 1 -6x 2

4. Polynomials Binomial is a Polynomial with two terms. Example: x + 5x 2 – 64y 2 – 5y Trinomial is a Polynomial with three terms. Example: x 2 – 2x +33z 2 – 6z + 7

5. Degree of Term Degree of Term of a polynomial in one variable is the exponent on the variable in that term Example: 4x 2 Second 2y 5 Fifth -5xFirst can be written -5x 1 3Zerocan be written 3x 0

6. Degree of Polynomial Same as that of its highest-degree term Example: 8x 3 + 2x 2 – 3x + 4 Third x 2 - 4Second 6x - 5First 4Zero x 2 y 4 + 2X + 3Sixth ( sum of exponents ) More than 2 variables then add the exponent of highest degree

7. Add Polynomials There are two ways to add polynomials: Horizontal expressions and Vertical (Column) form. To add Polynomials combine the like terms. Example: (7a 2 + a – 6) + (10a 2 – 3a + 9) 7a 2 + a – 6 + 10a 2 – 3a + 9 17a 2 – 2a + 3

8. Add Polynomials Example: (5x 2 + 2x + y) + (x 2 – 4x + 5) 5x 2 + 2x + y + x 2 – 4x + 5 6x 2 – 2x + y + 5 Example: (5a 2 b + ab + 2b) + (7a 2 b – 3ab – b) 5a 2 b + ab + 2b + 7a 2 b – 3ab – b 12a 2 b – 2ab + b

9. Add Polynomials in Columns Arrange the polynomial in descending order, one under the other with the like terms in the same column. Add the terms in each column Example:

10. Add Polynomials in Columns Example: (4x 3 + 3x – 4)+(4x 2 – 5x – 7)

11. Subtract Polynomials Use the distributive property to remove the parenthesis (this will change the signs in the second polynomial) Combine like terms

12. Subtract Polynomials Example: (4x 2 – 3x + 6) - (x 2 – 7x + 8) 4x 2 – 3x + 6 - x 2 + 7x – 8 4x 2 – x 2 – 3x + 7x + 6 – 8 3x 2 + 4x – 2

13. Subtract Polynomials Do we represent “subtract a from b” as a – b or b – a? b - a Example: Subtract (-x 2 – 4x + 2) from (x 3 + 3x + 9) (x 3 + 3x + 9) - (-x 2 – 4x + 2) x 3 + 3x + 9 + x 2 + 4x – 2 x 3 + x 2 + 3x + 4x + 9 – 2 x 3 + x 2 + 7x + 7

14. Subtract Polynomials in Columns Write the polynomial being subtracted below the polynomial from which it is being subtracted. List the like terms in the same column. Change the sign of each term in the polynomial being subtracted. Add the terms in each column.

15. Subtract Polynomials in Columns Example: Subtract (x 2 – 5x + 4) from (4x 2 + 7x + 6)

16. Subtract Polynomials in Columns Example: Subtract (3x 2 – 8) from (-4x 3 + 7x – 5)

17. Remember When adding drop the parentheses and combine the like terms. When subtracting use the distributive property to change the signs in the second polynomial. You can only evaluate and simplify a polynomial because they are expressions. You can NOT solve a polynomial because it is not an equation.

18. HOMEWORK 4.4 Page 266 - 267 #53, 57, 63, 69, 89, 97, 103