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# Polynomials Lesson

### Monomial

### Examples

### Coefficient of a Monomial

### Examples

### Degree of a Monomial

### Examples

### Polynomial

### Example

### Terms in a Polynomial

### Example

### Constant Term in a Polynomial

### Example

### Degree of a Polynomial

### Example

### Descending Power of One Variable in a Polynomial

### Example

### Ascending Power of One Variable in a Polynomial

### Example

### Similar Terms or Like Term

### Example

### Combination of Similar Terms

### Example

### Rules of Combining Similar Terms

### Example

### Rules of Remove Parenthesis (Addition of Polynomial)

### Example

### Rules of Remove Parenthesis (Subtration of Polynomial)

### Example

### Rules of Adding Parenthesis ("+" in Front of Parenthesis)

### Example

### Rules of Adding Parenthesis ("-" in Front of Parenthesis)

### Example

Monomial is an algebra expression in which there is only the product of number and variables.

The product of number and positive exponent of variables. Only a number or a variable is also a monomial.

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

The sum of exponent of all variables in a monomial is called the degree of the monomial.

For monomial 2x^{3}y^{2}, 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 2x^{3}y^{2} has the degree of five.

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

Each monomial is called a term of the polynomial.

polynomial 9x^{2} - 6x + 1 has three term, first term is 9x^{2}, second term is -6x, the third term is 1.

A term which has no any variable is called a constant term.

In polynomial 2x + 3, the constant term is 3.

The degree of a polynomial is the largest degree of any term.

polynomial 5y^{2} + 8y - 6 has three terms, the first term is 5y^{2}, 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.

Order a polynomial as descending power of one variable with the term of largest degree of that variable first.

Order a polynomial as ascending power of one variable with the term of the lowest degree of that variable first.

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.

2x^{2} and 6x^{2} are similar (like) terms, +3y and -2y are similar (like) terms, +6 and +5 are similar (like) terms.

In a polynomials, combine similar terms into only one term is called combination of similar term.

when add similar (like) terms, we only add their coefficient and keep variable and exponent the same, 3y + (-2y) = 3y - 2y = y.

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.

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.

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.

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.

If there is a "+" sign in front of the parenthesis, each term inside the parenthesis keep the same sign.

If there is a "-" sign in front of the parenthesis, every term inside the parenthesis must has its sign changed to its opposite sign.

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