3.1 Adding and Subtracting Polynomials BobsMathClass.Com Copyright © 2010 All Rights Reserved. 1 The degree of a polynomial is the degree of the term with the highest degree in the polynomial. The degree of a monomial is the sum of all exponents for each variable. The section will cover adding and subtracting polynomials. A polynomial is an algebraic expression that is a sum of terms, where each term contains only variables with whole number exponents and integer coefficients. A polynomial with one term is called a monomial, two terms is called a binomial, and three terms is called a trinomial. Polynomials with four or more terms are usually just called polynomials. The procedure for adding and subtracting will be to add like terms. Terms are like terms if they have the same variables with the same exponents on the variables. Final answers with more than one term are to be left in descending order. The highest degree term to the lowest degree term. If the degrees of two terms are equal, the order will be alphabetical, i.e, 5a + 2b.

3.1 Adding and Subtracting Polynomials BobsMathClass.Com Copyright © 2010 All Rights Reserved. 2 Your Turn Problem #1 Your Turn Problem #2

3.1 Adding and Subtracting Polynomials BobsMathClass.Com Copyright © 2010 All Rights Reserved. 3 (Now we can add our like terms) Your Turn Problem #3 There are two methods for subtracting polynomials, the horizontal method and the vertical method. First we will use the horizontal method. Then lesson will show both methods. Choose whichever you are comfortable with. Solution:

3.1 Adding and Subtracting Polynomials BobsMathClass.Com Copyright © 2010 All Rights Reserved. 4 Solution: Your Turn Problem #4

3.1 Adding and Subtracting Polynomials BobsMathClass.Com Copyright © 2010 All Rights Reserved. 5 (Rewrite the second polynomial above the first polynomial while lining up the like terms) (Second, change all the signs of the bottom polynomial to change the operation to addition) (Third, add the like terms) The following example will show the vertical format of subtracting polynomials. Solution:  Your Turn Problem #5 Write the sum of 8 and 5 first. Translating may involve more than one operation. Then, “subtract 4” will be written second. Now we can simplify once the problem has been translated.

3.1 Adding and Subtracting Polynomials BobsMathClass.Com Copyright © 2010 All Rights Reserved. 6 Solution: 1 st translate. Now simplify. Your Turn Problem #6 Note: if parenthesis are preceded by a + sign, the signs of all the terms will stay the same when we drop the parenthesis. However if the parenthesis are preceded by a - sign, the signs of all the terms will change when we get rid of the parenthesis.

3.1 Adding and Subtracting Polynomials BobsMathClass.Com Copyright © 2010 All Rights Reserved. 7 Solution: 1 st get rid of the parentheses. Next, add all like terms. Your Turn Problem #7

3.1 Adding and Subtracting Polynomials BobsMathClass.Com Copyright © 2010 All Rights Reserved. 8 When using grouping symbols within other grouping symbols, we usually use brackets for the outermost set of grouping symbols and parenthesis for the innermost set of grouping symbols. Order of operations tells us to take care of the innermost parenthesis first. 2. Get rid of the brackets. Note: it would also be fine to add like terms inside brackets first. 1. Get rid of the parenthesis by distributing the negative sign. Solution: Your Turn Problem #8 The End. B.R