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Polymomial Division 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 2x³.

Difference of Two Squares (Formular)

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Difference of Two Cubes (Formular)

Example

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.

Example

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