Factor calculator allows factoring online an algebraic expression, to achieve factoring an expression algebraic
online different methods are used:
The factoring calculator then returns the factorized form of the algebraic expression placed in parameter.
Factoring online by searching for common factors
The factoring calculator is able to recognize the common factors of an algebraic expression :
- These common factors can be number: Factoring the expression `3x+3`,
factor(3x+3), return `3(1+x)`
- These common factors can be letters, so factoring expression has `ax+bx`,
factor(ax+bx), return `x*(a+b)`
- These common factors can be algebraic expressions, so factoring expression has `(x+1)(x+2)+(3x+3)(x+1)`
factor((x+1)(x+2)+(3x+3)(x+1))
will return the following expression factorized `(x+1)*(5+4*x)`
Factorization using the special expansions
The factoring calculator is able to recognize the outstanding common identities and using them to factor
algebraic expressions.
- the following special expansion `a^2+b^2+2ab=(a+b)^2` is used to factor the expression `1+2x+x^2`,
The result returned by the function is `(1+x)^2`
- the following special expansion `a^2+b^2-2ab=(a-b)^2` is used to factor the expression `1-2x+x^2`
factor(1-2x+x^2),
the result returned will be the expression following factored `(1-x)^2`
- the following special expansion `a^2-b^2=(a-b)*(a+b)` is used to factor the expression `1-x^2`,
The result returned by the function is `(1-x)(1+x)`
Online factoring quadratics polynomials
Factor calculator is able to recognize quadratics polynomials and factoring them when possible.
- Thus, the function allows to factor online the following quadratic polynomial `-6-x+x^2`,
the result returned by the function is the expression factored `(2+x)*(-3+x)`
- For example by typing
factor(-1/2+x/2+x^2),
returns online factorization of quadratic polynomial ie `(1+x)*(-1/2+x)`
- For getting the factored form of the following polynomial `-21+4*x+x^2`, simply type factoring
factor(-21+4*x+x^2),
then the function returns the factorization of the quadratic polynomial `(7+x)*(-3+x)`
Factoring fractions
The factoring calculator is able to factor algebraic fractions with steps :
- Thus, the factoring calculator allows to factorize the following fraction `(x+2*a*x)/b`,
the result returned by the function is the factorized expression `(x*(1+2*a))/b`
- For example by entering factor((-1/2+x/2+x^2)/b),
the function will return the online factorisation of the fraction, i.e. `((1+x)*(-1/2+x))/b`
- To obtain the factorised form of the following fraction `(-21+4*x+x^2)/(1+2*x+x^2)`, simply enter
factor((-21+4*x+x^2)/(1+2*x+x^2)),
the function will then return the factorisation of the fraction of the polynomials of the 2nd degree `((7+x)*(-3+x))/((1+x)^2)`
- The expression to be factorized `(-21+4*x+x^2)/(1+2*x+x^2)` has a fractional form, so we factor the numerator and then the denominator.
- The expression to factor `-21+4*x+x^2` is a second degree polynomial.
- The polynomial admits two roots `-7` and `3` : equation_solver(-21+4*x+x^2)
- The factored form of the polynomial is `(7+x)*(-3+x)`.
- The expression to factor `1+2*x+x^2` is a special expansion type `a^2+b^2+2*a*b`, with `a=1` and `b=x`
- The factorization of `a^2+b^2+2*a*b` is `(a+b)^2`
- By replacing a by `1` and b by `x`, we obtain the factored form of the expression, ie `(1+x)^2`.
- The factorization of the fraction `(-21+4*x+x^2)/(1+2*x+x^2)` is therefore `((7+x)*(-3+x))/(1+x)^2`
Games on factoring
The site offers quizzes on factoring that allow you to practice factoring many forms of expressions.