Summary :

The factoring calculator allows to factor an algebraic expression online with steps.

Description :

Factoring calculator with steps

Factor calculator allows factoring online an algebraic expression, to achieve factoring an expression algebraic online different methods are used:

• Factoring by search common factors
• Factorization using special expansions
• Factoring online quadratic polynomials
• Factoring fractions

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`, factoring_calculator(`3x+3`), return `3(1+x)`
• These common factors can be letters, so factoring expression has `ax+bx`, factoring_calculator(`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)` factoring_calculator(`(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` factoring_calculator(`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 factoring_calculator(`-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 factoring_calculator(`-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 factoring_calculator(`(-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 factoring_calculator(`(-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)`

Syntax :

Examples :

Factorize an identity

• factoring_calculator(`1+2x+x^2`) returns `(x+1)^2`.
• factoring_calculator(`1-x^2`) returns `(1-x)(1+x)`

Factor an expression

• Factoring expression (2+2*x+(x+1)*(x+3)) with the function factoring_calculator(`(2+2*x+(x+1)*(x+3))`) returns `(x+5)*(1+x)`

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