Nomial is another name for number or term. Poly means many. A polynomial is many numbers or many terms.
In algebra 1 we work with:
Monomials - - which means one term
Examples:
5
x
12y
-8xyz
Binomials - - which means two terms
Examples:
2x - 6
x + y
-8xyz + 12x
Notice that binomials are in
lowest terms and have no like terms that can be combined.
Trinomials - - which means three terms
Examples:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiZ2ScSEMlbBBebCkEVeiOmhsiZd7V8dLs7E5vuurijt12bEZ86qALZsdYz3iyXSYVpr5E3GUC4MmMrYov7zvQGhHfScKNu10DY2hDcXwuedo7tCeGZ5DWwXq5mpwochlTktWU-ZhFbqgR2/s320/tri.jpg)
Each of these polynomials also has a DEGREE (or power). We find the degree by finding the highest power of each term. The term with the highest power sets the degree for the polynomial.
Polynomials can be:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiqGXo67PIyXDzzVH4rV3w2_whi2tkQAmwyZkqd_vyz4VSnptbUDq9-CXx-uzDl_QAnuBqV68Aogeicufsk01i57-r0g35IM1Z6EWpSpWZStUS2AEDbS5Ur1bZ934cZPyTj6fTYCekQ8HXC/s320/drg.jpg)
constant
(0 degree)
linear
(1st degree)
quadratic
(2nd degree)
cubic (3rd degree)
4th degree
5th degree
and on and on.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiyy0VMzX0-tUfJgnC3AmPK9aH4MZ7yi_typ0rE86q33e_MzVleQKrHxk5U__1gsyfDt4eazIVEPcWVr_FHfv7sQqdJxg_h87b8XjdYc6T_Zvi-WRhpBO6mrZcqe86-Qpmw4dvMeuXpwxuT/s320/comb.jpg)
However, the highest degree of a polynomial is the combination of the powers in each individual term.
Standard Form of a PolynomialAs we have learned this year, there are specific ways to write algebraic terms. When writing polynomials we write them from the highest exponent to the lowest exponent.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgx_xUZP5FUBZUv_DLWRQzli7wPo2PE-KMs6T6xfCcF42Ow3eYpUuVH8cx_J11ExCgX6GHfaF2zsWzPda5ODpXQd_D3kd3w-KmTen6d4v7p0y22-EOZkgwvo819wJGCaavYTJQYUafx1K9A/s320/stand.jpg)
They are also written in reduced form so all mathematical process that
can be done,
must be done and all like-terms must be combined so the polynomial is in standard form.
Your final answer must be written in standard form, in lowest term.
Adding Polynomials![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjT-rg7Q3LZVwmX07F49nFOPpYzeUa4DnWxG3oLNxdAnXZaaaVfoMbZZMuhOgsEkm-Zjj-brGwgLi2XORIQtLXscTic9nxdopzU1W0LaaLvRib7FR7NG4G5Itv71M41GR-S97bKKoxEBnlH/s320/ad.jpg)
Adding vertically may be the easiest procedure:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiFVvXyEyjBVLgTP1oDMkYkwG7CSucxG-Ec1D69vJ9l7s8PHP0pWBFKS8NJyhREql4rTYRmstymHtD2swjx3Ri5eWXJlE2WLd7oj5Dig1m0i1w80xcyoboK_PHzG9ZxUWQlZvyq-41j0i6N/s320/add.jpg)
Remember to line up like terms so you are combining like variable with the same exponent.
Subtracting Polynomials![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgaCesrP0_1Hk286ccxdPCOYi6JfXXWO5Tw85U6-GEQ_n8jXwkWLpCS4JM9y3YAcB2zwQ2SBPChmGUnGu5F9cBTfy_piGrz0vxZinZkVi9JpsTkB9XR6It9bh39NrVocFc9XARMOrzPi0ta/s320/sub.jpg)
You must remember to distrbute the negative sign into the parentheses.