Section 5.2

1. Section 5.2 • Addition and Subtraction of Polynomials

2. Polynomial Page 307 A term is a number, a variable, or the product or quotient of a number and one or more variables raised to powers. The number in the product is called the numerical coefficient, or just the coefficient. 8k38 is the coefficient-4p5–4 is the coefficient

3. Polynomial Page 307 A polynomial is a term or a finite sum of terms in which all variables have whole number exponents and no variables appear in denominators. Polynomials Not Polynomials

4. Example Page 307-8 • Determine whether the expression is a polynomial. If it is, state how many terms and variables the polynomial contains and its degree.(The degree of monomial is the sum of the exponents of the variables. If the monomial has only one variable, its degree is the exponent of that variable.) • The expression is a polynomial with three terms and one variable. The term with the highest degree is 9y2, so the polynomial has degree 2. • b. The expression is a polynomial with four terms and two variables. The term with the highest degree is 2x3y2, so the polynomial has degree 5. • c. The expression is not a polynomial because it contains division by the polynomial x + 4.

5. Example Page 309 • State whether each pair of expressions contains like terms or unlike terms. If they are like terms, then add them. • 9x3, −2x3 • b. 5mn2, 8m2n The terms have the same variable raised to the same power, so they are like terms and can be combined. 9x3 +(−2x3) = (9+(−2))x3 = 7x3 The terms have the same variables, but these variables are not raised to the same power. They are therefore unlike terms and cannot be added.

6. Example Page 309-10 • Add by combining like terms. • Solution

7. Example Page 310 • Simplify. • Solution • Write the polynomial in a vertical format and then add each column of like terms.

8. Page 310 Subtraction of Polynomials • To subtract two polynomials, we add the first polynomial to the opposite of the second polynomial. To find the opposite of a polynomial, we negate each term.

9. Example Page 311 • Simplify. • Solution • The opposite of

10. Example Page 311 • Simplify. • Solution

11. Problem 40 Combine like terms

12. Problem 66 Add the opposite of the polynomial being subtracted.

13. Problem 67 Add the opposite of the polynomial being subtracted.

14. Problem 76 Number 76 Area of a Rectangle: Write a polynomial that gives he area of the rectangle. Calculate its area for x=3 feet. 7 x 3x

15. DONE

16. Objectives • Monomials and Polynomials • Addition of Polynomials • Subtraction of Polynomials • Evaluating Polynomial Expressions

17. Monomials and Polynomials A monomial is a number, a variable, or a productof numbers and variables raised to natural number powers. Examples of monomials: The degree of monomial is the sum of the exponents of the variables. If the monomial has only one variable, its degree is the exponent of that variable. • The number in a monomial is called the coefficient of the monomial.

18. Example • Write a monomial that represents the total volume of three identical cubes that measure x along each edge. Find the total volume when x = 4 inches. • Solution • The volume of ONE cube is found by multiplying the length, width and height. • The volume of 3 cubes would be:

19. Example (cont) • Write a monomial that represents the total volume of three identical cubes that measure x along each edge. Find the total volume when x = 4 inches. • Solution • Volume when x = 4 would be: • The volume is 192 square inches.