Factor a polynomial
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.
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)`.
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 :
|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')