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
x+5
x2
x1
x0
2x2
4x
6
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
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
3n4
5n3
3n4
7n3
12n3
n2
n1
n0
8n
7n2 -4n
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
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
5n3
-3n3
2n3
n2
n1
n0
-6n2
6
+-4n2
+-2
-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