Free Homework Math Help: Factoring Methods

Factoring Methods

According to the Fundamental Theorem of Algebra:

A polynomial of degree n has at least one complex zero.

Also, according to the Linear Factor Theorem:

A polynomial of degree n can be written as the product of n linear factors.

Solving polynomials by factoring depends on the Zero Factor Theorem:

If ab = 0 then a = 0 or b = 0.

However, according to the Factorization Theorem:

If a trinomial ax² + bx + c has a, b and c as integers then its factors will have integers if and only if the square root of b² - 4ac is an integer.

In other words, b² - 4ac has to be a perfect square.

In addition there are certain conditions to keep in mind when factoring polynomials:

1. The constant c is the product of the constants in the factors.
2. In a trinomial, the middle coefficient b is the sum of the binomial constants in the factors.
3. In a trinomial, the binomial constants in the factors will have the same sign as the middle coefficient b if the trinomial constant c is positive.
4. If the trinomial constant c is negative, the binomial factors will have opposite signs.
5. If there are no common factors in the terms of a polynomial, the factors of the polynomial will not have a common factor.

The first step to perform when factoring polynomials is to factor out all the common factors. The next step would be to apply one of the following factoring methods.

1. Factoring by Grouping
2. Trial Method
3. Table Method or ACDD
4. Special Factoring Formulas
5. Completing the Square
6. Quadratic Formula