back to *algebra*
# 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**