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# Polymomial Division and Factoring Polynomials

### Divide a Monomial By a Monomial

### Example

### Polynomial Divide By Monomial

### Example

### Factoring Polynomials

### Example

### Factorable Polynomials

### Example

### Not Factorable Polynomials

### Example

### Common Factors

### Example

### Greatest Common Factors (GCF) If The Terms Have No Common Variable Factors

### Example

### Greatest Common Factors (GCF) If The Terms Have Common Variable Factors

### Example

### Difference of Two Squares (Formular)

### Example

### Difference of Two Cubes (Formular)

### Example

### Sum of Two Cubes (Formular)

### Example

### Factoring Polynomials By Grouping

### Example

### Factoring Polynomials By Combing Methods

### Example

### Factoring Trinomials

### Examples

To divide a monomial by a monomial, divide coeffcients and similar base respectively, if there is a single variable in the denominator, keep this variable and its exponent as a factor of the quotient.

Divide each term of the polynomial by the monomial, if there is a single variable in the denominator, keep this variable and its exponent as a factor of the quotient.

To represent a polynomial as a product of two or more polynomials. Each polynomial that is multiplied to form the product is called a factor of the product.

The factors of the product x (x + y) (x - y) are x, (x + y) and (x - y)

The polynomial can be represented as a product of two or more factors.

The polynomial shown below can be factoring as a factor of x and (x + y).

The polynomial can not be represented as a product of factors. For example, right side polynomial can not be factored.

The factor is common in each term of the polynomial, for example, x is the common factor of the right side of the polynomial.

GCF is the largest integer that is a factor of all the coeffients of the polynomials.

The GCF is the monomial with the largest integer exponent that is a factor of the polynomial.

The greatest common factors of the polynomial shown above is the monomial 2x^{3}.

To factor polynomials, first group the terms of the polynomials, and then look for common polynomial factors in each group.

Steps (1). Factor out common factors. (2). Examine if you can apply formulas to factor the remaining polynomial. (3). Determine if factoring by grouping can be applied.

To factor trinomials follow these rules: (1). The product of the first term of each binomial is ax^{2}. (note: the symbol x^{2} represent x square).
(2). The sum of the product of the outside terms and the product of the inside terms is bx. (3). The product of the last terms is c.

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