This documents is a summary of the Algebraic Expression topic under College Algebra. This will discuss what is Algebraic Expression, different Algebra terms, and how to simplify or solve polynomials.
In Algebra letters can be used to represent a number.
Constant- if the letter has only one value.
Variable- if more than one value from a given set of allowable values.
Algebraic Expression refers to a constant, variable, or a combination of variables and constant involves fundamentals
operations such as addition, subtraction, multiplication, division, exponentiation, and extraction of roots.
Term in Algebraic Expressions
-the distinct part together with the sign is called a term.
Example of algebraic equation: 9x2 + 10x + 3
Where:
1. 9x2, 10x, and 3 are all example of terms
2. 9, 10, and 3 are coefficient
3. x is the variable
4. 2 is the exponent
Monomial – “mono” means one, thus if the expression has only one term, it called monomial. Going back to the
example above, the 9x2 alone is called monomial.
Binomial – “bi” means two, thus if the expression has two term it called binomial. Going back to the example above, the
10x + 3 is called binomial.
Trinomial – “tri” means three, thus if the expression has two term it called trinomial. Going back to the example above,
the 9x2 + 10x + 3 is called trinomial.
Polynomials
-Polynomials is also a group of terms. “poly” means many so it means many terms.
-Polynomials is a sum of finite number of terms where each terms have coefficients, being multiplied by a variable and
being raised by a non-negative integer power.
Example of non-polynomial: 5x-2 + 10x + 3
Explanation: As you can see in the example, the coefficient 5 is being multiplied by variable x, and being raised by
negative 2. This equation is not considered as polynomial because it is raised by a negative integer.
1. FUNDAMENTAL OPERATIONS ON POLYNOMIALS
1.2 Addition and Subtraction of Polynomials
-we only add or subtract terms with similar variable and exponent
Example. Simplify 12a2 + 4a – 6a2 + 9a
Adding coefficients of similar terms:
12a2 + 4a – 6a2 + 9a = (12-6) a2 + (4+9) a
= 6a2 + 13a
Explanation: In this example we cannot add the term 12a2 to term 4a or to 9a, even though they have the same variable,
but they have different exponent.
1.2 Multiplication of Polynomials
-in multiplication of polynomials we add the exponents of the terms with the same base.
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller leahregorgo. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $8.34. You're not tied to anything after your purchase.
