Section 5.4: Adding and Subtracting Polynomials Worksheet 5.4
Vocab: A monomial is a product of numbers and variables.
Examples: The following are all monomials.
$-5$
$x$
$A$
$5x$
$7xy$
$\frac{3}{2}x^2 y z^3$
Examples: The following are NOT monomials.
$\frac{1}{x}$
$A^{-1}$
$\frac{5}{x^2}$
$7xy^{-2}$
Single Variable Monomials
A monomial in a single variable has the form $a x^{n}$
Vocab: For the monomial $a x^{n}$, $a$ is called the coefficient, and $n$ is the
degree of the monomial.
Example: $4x^7$
Polynomials
Vocab: A polynomial is a sum of monomials.
Examples
$-5$,
$2xy$
$3x^2+2xy-5y^2$
The following is a single variable polynomial: $2x^5+\frac{4}{5}x^3-x^2+x-9$
Vocab: The highest exponent for a single variable polynomial is called
the degree of the polynomial.
More Vocab: Every monomial in a polynomial is called a term.
Example: $2x^5+\frac{4}{5}x^3-x^2+x-9$
Degree? How many terms?
What is the coefficient on the 3rd degree term?
One More Piece of Vocab: A polynomial with 1 terms is called a ???.
One More Piece of Vocab (Okay, I lied.): A polynomial with 2 terms is called a binomal.
One More Piece of Vocab (I lied again.): A polynomial with 3 terms is called a trinomal.
For the rest of the semester we'll be learning to handle polynomials in either one or two variables.
Today, we learn how to add and subtract polynomials in a single variable.
Adding Polynomials
To add polynomials, simply add like terms.
Like terms have the same degree.
Example: $( -2z^4+ 3z^2+ 2z+ 6)+( 7z^4 -3z^3-9z+ 9)$
Subtracting Polynomials
To subtract polynomials, subtract like terms.
You may also change the sign of every term in the polynomial being subtracted and simply add.
Example: $( 4r^3+ 8r^2 -2r+ 3)-( -3r^2+ 9r+ 2)$
Note: In the homework, if you see an empty set of parentheses $()$ , treat it like 0.