Vocabulary
Factored Completely- A factorable polynomial with integer coefficients is factored completely if it is written as a product of unfactorable polynomials with integer coefficients.
Factor by Grouping- To factor a polynomial with four terms by grouping, factor common monomials from pairs of terms and then look for a common binomial factor.
Quadratic Form- The form au² + bu + c, where u is any expression in x.
Factor by Grouping- To factor a polynomial with four terms by grouping, factor common monomials from pairs of terms and then look for a common binomial factor.
Quadratic Form- The form au² + bu + c, where u is any expression in x.
Essential Information
Polynomials with a degree greater than 2 can also be factored, some can be factored completely using some of the techniques.
Factoring Polynomials
A factorable polynomial with integer coefficients is factorable completely if it is written as a product of unfactorable polynomials with integer coefficients.
Factoring Polynomials
A factorable polynomial with integer coefficients is factorable completely if it is written as a product of unfactorable polynomials with integer coefficients.
Factoring Patterns
There are also two factoring patterns that can be used to factor the sum or difference of two cubes.
Special Factoring Patterns
There are also two factoring patterns that can be used to factor the sum or difference of two cubes.
Special Factoring Patterns
- Sum of Two Cubes a³ + b³ = (a + b)(a² - ab + b²)
- Difference of Two Cubes a³ - b³ = (a - b)(a² + ab + b²)
Factoring by Grouping
Some polynomials can be factored by grouping pairs of terms that have a common monomial factor.
Some polynomials can be factored by grouping pairs of terms that have a common monomial factor.
Quadratic Form
An expression of the form au² + bu + c, where u is any expression in x, is said to be in quadratic form. The factoring techniques can be used to factor such expressions.
An expression of the form au² + bu + c, where u is any expression in x, is said to be in quadratic form. The factoring techniques can be used to factor such expressions.
Solving Polynomial Equations
The zero product property is used to solve factorable quadratic equations, this can be easily extended to higher degree polynomial equations.
The zero product property is used to solve factorable quadratic equations, this can be easily extended to higher degree polynomial equations.