Factoring Polynomials Calculator


With this calculator, you can obtain the factored version of a polynomial if it is possible. The entered expression will be returned as a multiplication of its various factors or as a binomial raised to an exponent.

How to use the polynomial factorization calculator?

Step 1: Enter the polynomial in the corresponding input box. You must use * to indicate multiplication between variables and coefficients. For example, instead of entering 2x^2+2x, enter 2*x^2+2*x.

Step 2: Click “Factor” to get the factored version of the input polynomial, if possible.

Step 3: The solution along with the entered polynomial will be displayed at the bottom. If the polynomial cannot be factored, it will simply be displayed in its original form or a simplified form if possible.

How to enter polynomials in the calculator?

To enter polynomials you must use the * sign to indicate multiplication between variables and coefficients. Also, you must use the ^ sign to indicate an exponent. For example,

  • To write \(x^3+5x+2\), enter x^3+5*x+2.
  • To write \(4x^3+3x^2+3x\), enter 4*x^3+3*x^2+3*x.
  • To write \(\frac{1}{4}x^3+\frac{1}{3}x^2+\frac{1}{3}x\), enter 1/4*x^3+1/3*x^2+1/3*x.

As you can see in the third example, we can also enter fractional coefficients. To do this, simply write the fraction in the form 1/2*x, which indicates one-half of x.

Is it possible to calculate factors of cubic polynomials and higher degrees?

As long as the polynomial does have factors, the calculator can factor polynomials of any degree. The polynomial must be valid, that is, it must contain only positive integer exponents.

What is polynomial factorization?

Factoring is the process of writing polynomials as a multiplication of unique polynomials of a lower degree, which produce the original polynomial when multiplied.

For example, consider the polynomial \(x^3+6x^2+11x+6\). Its factored form is \((x+1)(x+2)(x+3)\). This means that if we multiply all the terms in the factored version, we will get the original polynomial.

Another example is the polynomial \(x^3+9x^2+27x+27\). Its factored form is \((x+3)^3\). In this case, we see that its factored version is a cubed binomial. This simply means that you have a factor that repeats three times. That is, we have \((x+3)(x+3)(x+3)\).

What is polynomial factorization useful for?

Polynomial factorization can be useful for finding the roots of a polynomial. For example, if we have the polynomial \( x^2+3x+2\), we can factor it to get \( (x+2)(x+1)\). In this factored form, we can easily deduce that the roots of the polynomial are \( x=-2, ~x=-1\).

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