Polynomial Factorization Calculator


Input Examples
  • \(\displaystyle \small{x^2+5x+6\rightarrow} \) x^2+5x+6
  • \(\displaystyle \small{x^2-\frac{5}{3}x-\frac{2}{3}\rightarrow} \) x^2-(5/3)x-(2/3)
  • \(\displaystyle \small{x^2+2xy+y^2\rightarrow} \) x^2+2xy+y^2
  • \(\displaystyle \small{x^2+\left(a+b\right)x+ab}\rightarrow \) x^2+(a+b)x+ab
How to Use
  • You can use the characters \( \small{a,b,c,x,y,z} \).
  • Represent exponentiation with ^.
  • Use only () for parentheses.
  • Polynomial Expansion Calculator is available at this link.


What is factorization?

Factorization is the transformation of an expression expressed in the form of a sum into the form of a product.

The following is the basic formula for factorization.

\begin{align} &x^2+\left(a+b\right)x+ab=\left(x+a\right)\left(x+b\right)\\[+5pt] &x^2\pm 2xy+y^2=\left(x\pm y\right)^2\\[+5pt] &x^2-y^2=\left(x+y\right)\left(x-y\right) \end{align}


Example

Example 1

Factorize \(\displaystyle x^2+4x+4 \).

Solution

\[ x^2+4x+4=\left(x+2\right)^2 \]


Example 2

Factorize \(\displaystyle 25x^2-16y^2 \).

Solution

\[ 25x^2-16y^2=\left(5x+4y\right)\left(5x-4y\right) \]