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Polynomials Lesson
Monomial
Monomial is an algebra expression in which there is only the product of number and variables.
Examples
The product of number and positive exponent of variables. Only a number or a variable is also a monomial.
Coefficient of a Monomial
The number in a monomial is called the coefficient of the monomial.
Examples
Degree of a Monomial
The sum of exponent of all variables in a monomial is called the degree of the monomial.
Examples
For monomial 2x3y2, the exponent of variable x is 3, and the exponent of variable y is 2, the sum of the exponents x and y is 5, therefor, monomial 2x3y2 has the degree of five.
Polynomial
The sum of one or more monomial is called polynomial. Monomial is a special case of polynomial.
Example
Terms in a Polynomial
Each monomial is called a term of the polynomial.
Example
polynomial 9x2 - 6x + 1 has three term, first term is 9x2, second term is -6x, the third term is 1.
Constant Term in a Polynomial
A term which has no any variable is called a constant term.
Example
In polynomial 2x + 3, the constant term is 3.
Degree of a Polynomial
The degree of a polynomial is the largest degree of any term.
Example
polynomial 5y2 + 8y - 6 has three terms, the first term is 5y2, the variable y has an exponent of 2, so the first term has degree of 2,
second term is 8y, the variable y has exponent of 1, so the second term has degree of 1, the third term is a constant, so the degree of the
third term is zero. Therefore, the degree of this polynomial is 2, it is two degree three terms polynomial.
Descending Power of One Variable in a Polynomial
Order a polynomial as descending power of one variable with the term of largest degree of that variable first.
Example
Ascending Power of One Variable in a Polynomial
Order a polynomial as ascending power of one variable with the term of the lowest degree of that variable first.
Example
Similar Terms or Like Term
If two or more terms in a polynomial have the same veriable name and the same variable name has same exponent, then these terms are similar (like) terms. Constant terms are similar (like) terms.
Example
2x2 and 6x2 are similar (like) terms, +3y and -2y are similar (like) terms, +6 and +5 are similar (like) terms.
Combination of Similar Terms
In a polynomials, combine similar terms into only one term is called combination of similar term.
Example
when add similar (like) terms, we only add their coefficient and keep variable and exponent the same, 3y + (-2y) = 3y - 2y = y.
Rules of Combining Similar Terms
Add coefficient of all similar terms in a polynomial, the result is the new coefficient of the term in which variables name and the exponent of variable name keep the same.
Example
If two similar terms have opposite coefficient, the combination of the two terms is zero. If there is no similar terms in a polynomial, you need to keep the term for this polynomial.
Rules of Remove Parenthesis (Addition of Polynomial)
If there is a "+" sign in front of the parenthesis, each term inside the parenthesis keep the same when remove the parenthesis and the "+" sign in front of the parenthesis.
Example
Rules of Remove Parenthesis (Subtration of Polynomial)
If there is a "-" sign in front of the parenthesis, every term inside the parenthesis must has its sign changed to its opposite sign when remove the parenthesis and the "-" sign in front of parenthesis.
Example
Rules of Adding Parenthesis ("+" in Front of Parenthesis)
If there is a "+" sign in front of the parenthesis, each term inside the parenthesis keep the same sign.
Example
Rules of Adding Parenthesis ("-" in Front of Parenthesis)
If there is a "-" sign in front of the parenthesis, every term inside the parenthesis must has its sign changed to its opposite sign.
Example
