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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.

What is the monomial?

Coefficient of a Monomial

The number in a monomial is called the coefficient of the monomial.

Examples

What is the coefficient of a monomial?

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.

What is the degree of a monomial?

Polynomial

The sum of one or more monomial is called polynomial. Monomial is a special case of polynomial.

Example

What is the polynomial?

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.

What is the terms in a polynomial?

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.

What is the constant term in a polynomial?

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.

What is the degree of a 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

What is the descending power of one variable in a polynomial?

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

What is the ascending power of one variable in a polynomial?

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.

What is the similar terms or 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.

How to do the combination of similar terms?

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.

How to combining similar terms?

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

How to combining similar terms?

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

How to remove parenthesis?

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

How to remove a parenthesis?

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

How to adding parenthesis?