Factoring polynomial calculator - How to factor polynomials and find the greatest common divisor of polynomials

The pf command factors a polynomial or makes the expression in factored form. Input the command and polynomial in the form above and press the enter key. In this page, you can get the factored expression.

Factor a polynomial

If you want to factor x^{2}+3x+1, write the following code in the header form.

pf 2*x**2+3*x+1

The expression means

\[ 2 x^{2} + 3 x + 1 \]

Then press the enter key and you get this factored expression.

\[ \left(x + 1\right) \left(2 x + 1\right) \]

Note that you need write 3*x for expressing 3x. If you write 3x in the expression instead, this online calculator may return an incorrect output. It can't recognize the implicit multiplication (2x, 3x, etc). Double asterisks (**) means the power and the ^ symbol can't be used to mean the exponent.

Factoring polynomials is a basic approach to get the solution to a equation. The reversing process that simplifies a factored expression is called "expanding". Some polynomials can't be factored in the real number like this.

You cannot factor some polynomials in the real number

In the algebraic theory, all polynomials can be factored in the complex number and the degree of a polynomial is equal to the number of terms in the factored form.

Find the greatest common divisor of polynomials

You can find the GCD of polynomials using the gcd command as follows.

gcd x**2-5*x+4, x**2-1

The GCD of polynomials

All polynomials are separated by comma. The calculator won't work properly if the coefficients of argument polynomials are fractions or complex numbers. In the above example, the output is x-1 that both polynomials have as a greatest factor.