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`.

Quadratic Polynomials

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)`.

Factoring by Grouping

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.

How to use this calculator?

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'
Polynomial 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)
Examples 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')

See also

Polynomial calculators
Math Calculators