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# 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.
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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 2x3.
Difference of Two Squares (Formular)
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Difference of Two Cubes (Formular)
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Sum of Two Cubes (Formular)
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Factoring Polynomials By Grouping
To factor polynomials, first group the terms of the polynomials, and then look for common polynomial factors in each group.
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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.
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Factoring Trinomials
To factor trinomials follow these rules:
(1). The product of the first term of each binomial is ax2. (note: the symbol x2 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