# Polynomial Divide By Monomial and Factoring Polynomials

**Divide a Monomial By a Monomial**
- 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.

**Example**

**Polynomial Divide By Monomial**
- 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.

**Example**

**Factoring Polynomials**
- 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.

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

**Factorable Polynomials**
- The polynomial can be represented as a product of two or more factors.

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

**Not Factorable Polynomials**
- The polynomial can not be represented as a product of factors. For example, right side polynomial can not be factored.

**Example**

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

**Example**

**Greatest Common Factors (GCF) If The Terms Have No Common Variable Factors**
- GCF is the largest integer that is a factor of all the coeffients of the polynomials.

**Example**

**Greatest Common Factors (GCF) If The Terms Have Common Variable Factors**
- The GCF is the monomial with the largest integer exponent that is a factor of the polynomial.

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

**Difference of Two Squares (Formular)**

**Example**

**Difference of Two Cubes (Formular)**

**Example**

**Sum of Two Cubes (Formular)**

**Example**

**Factoring Polynomials By Grouping**
- To factor polynomials, first group the terms of the polynomials, and then look for common polynomial factors in each group.

**Example**

**Factoring Polynomials By Combing Methods**
- 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.

**Example**

**Factoring Trinomials**
**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.

**Examples**