ALGEBRAIC EXPRESSIONS
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.
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.
