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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 