4.2 and 4.3 Adding and Subtracting Polynomials MT4 covers a lot of territory and is a long topic. It is also a vital cog in completing the rest of your Algebra topics. Without mastery of the concepts in MT4, the rest of the Algebra topics will be unconquerable. The items that you will have to learn are… 4.2 and 4.3 Add and Subtract Polynomials 4.4 Exponent Rules 4.5 Multiply Polynomials 4.7 Factoring with Greatest Common Factor (GCF) 4.8 Difference of Two Squares Factoring 4.9 Diamond Method Factoring

4.2 and 4.3 Adding and Subtracting Polynomials We should start with some new vocabulary words. The first one is the word “Terms”. Terms are mathematical expressions separated by plus “+” or minus “-” signs. Here is one term… 3x2 Here are two terms… 5x + 3 Three terms… 6x3 – 4x2 + 1 Notice that terms can be separated by either a plus or a minus. Another new word is “Polynomial”. A polynomial is a math expression that has more than one term (poly means “many”). In this lesson we will be adding and subtracting polynomials. Let’s start…

4.2 and 4.3 Adding and Subtracting Polynomials A word problem will look like this… A squirrel ran around the outside of the fence. Write an expression that represents how far he ran. 2x2 + 4x + 6 x + 5 10x - 3 To Solve: Combine all the terms in the polynomials. We are going to create a table to keep track of our terms…

4.2 and 4.3 Adding and Subtracting Polynomials 2x2 + 4x + 6 x2 x1 x0 2x2 4x 6 x 5 x + 5 10x - 3 10x -3 2x2 15x 8 First, create a table with column headings x2, x1, x0. Always make enough columns that start with your largest exponent! If my largest exponent was x4, I would have five columns with the first column named x4. Now place your terms in the correct column. Be sure to remember that x0 means a number that has no “x’s”. Now combine your columns and you’ve got your answer… The squirrel travelled 2x2 + 15x + 8

Please add (3n4 + 8n + 5n3) and (7n3 + 7n2 – 4n) 4.2 and 4.3 Adding and Subtracting Polynomials Not all your questions will be word problems. Sometimes the problems will look just like this… Please add (3n4 + 8n + 5n3) and (7n3 + 7n2 – 4n) n4 n3 n2 n1 n0 3n4 5n3 8n 7n3 7n2 -4n 3n4 12n3 7n2 4n Make a table with 5 columns and 2 rows. The first column is the largest exponent, n4, and then go in descending order. Now place your terms in the correct columns! Now combine them… Your answer is….3n4 + 12n3 + 7n2 + 4n

(5n3 - 6n2 + 6) - (3n3 - 4n2 – 2) 5n3 -6n2 6 - + + 3n3 -4n2 -2 4.2 and 4.3 Adding and Subtracting Polynomials I know it seems so easy, and it usually is. The tricky part is when you are asked to Subtract the polynomials. They will look like this… (5n3 - 6n2 + 6) - (3n3 - 4n2 – 2) n3 n2 n1 n0 5n3 -6n2 6 - + + 3n3 -4n2 -2 2n3 -2n2 8 Again, make a table and start with the largest exponent (n3). Now place your terms in the correct columns! Now for the tricky part. The minus sign “-” makes you change all the terms in the second group to the opposite sign! Every positive is now a negative and every negative is now a positive. Now combine your like terms. Your answer is….2n3 - 2n2 + 8