Algebra for all the Grades

Factoring polynomials is the way of multiplying polynomials. if we divide the polynomial with the factors then the result will be zero.

Consider the identity a² - b² = (a + b)(a - b).In this identity a² - b² is the polynomial and a + b and a - b are the factors.

If we divide the polynomial with a + b or a - b then the remainder is 0.

Let us learn about factoring quadratic polynomial. Quadratic polynomial has three terms.They can be factored in three ways.

1. Factoring by grouping

2. completing the square

3. Using quadratic formula.

Factoring of polynomials

Some of the identities used while factoring polynomials are

• a² + 2ab + b² = (a + b)²
• a² - 2ab + b² = (a - b)²
• a² - b² = (a + b)(a - b)
• x² + x(a + b) + ab=(x + a)(x + b)
• a³ + b³ = (a + b)(a² - ab + b²)
• a³ - b³ = (a - b)(a² + ab + b²)

How to factor polynomials

The steps to factor a polynomial by grouping method.

Firstly if there is any common factor in all the terms in the given polynomial or try to find the GCD of all the terms in the polynomial and take it out and write the remaining terms in a (algebra-1-help).

Ensure that any above identities and try to write the factors.