# Factor a polynomial

This calculator computes a polynomial factorization.

## How to Factor a Polynomial?

Factoring a polynomial means expressing this polynomial as the product of several other polynomials of a lower degree. Factoring is essential in algebra for solving equations, simplifying expressions, and more.

### Simple Factoring

Start by looking for a common factor in all the terms of the polynomial. For instance, for 6x^2 + 12x, the common factor is 6x. So, this expression can be factored as 6x(x + 2).

### Recognizing special forms

Difference of squares: If you have an expression like a^2 - b^2, it can be factored into (a + b)(a - b).

Perfect square: If you have an expression like a^2 + 2ab + b^2 or a^2 - 2ab + b^2, they can be factored respectively into (a + b)^2 and (a - b)^2.

If you have a polynomial of the form ax^2 + bx + c, you can use the quadratic formula to find its roots r_1 and r_2. Once you have these roots, the polynomial can be factored as a(x - r_1)(x - r_2).
Sometimes, a polynomial can be rearranged and grouped to facilitate factoring. For example, for acx + ad + bcx + bd, you can group terms to get a(cx + d) + b(cx + d), which then gets factored into (a + b)(cx + d). Practice is key to mastering factoring. The more one practices identifying and working with these forms, the easier it becomes to factor polynomials quickly and efficiently.
Variable Input a single-letter that is the polynomial variable. Examples : polynomial = 4x+1 , then input variable = 'x' polynomial = 9t + 5 , then input variable ='t' Are accepted : The Polynomial variable Polynomial coefficients : must be rational numbers e.g. integer numbers (-4) or fractions (1/4) or decimals (3.6). Operators : + - * / ^ (the last is the power operator so x^2 = x^2) Parentheses : an example of use is (x^2+1)(x-5) Polynomial = x^2-4x+1 (variable = 'x') Polynomial = (x^2-1)(x-5)-3 (variable = 'x') Polynomial = x^3-4/3*x^2+1 (variable = 'x') Polynomial = 0.23*t^2-1/5*t+1/2 (variable = 't')