# 6x 12 factored

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### What is factoring?

A polynomial with rational coefficients can sometimes be written as a product of lower-degree polynomials that also have rational coefficients. In such cases, the polynomial is said to "factor over the rationals." Factoring is a useful way to find rational roots (which correspond to linear factors) and simple roots involving square roots of integers (which correspond to quadratic factors).

Polynomials with rational coefficients always have as many roots, in the complex plane, as their degree; however, these roots are often not rational numbers. In such cases, the polynomial will not factor into linear polynomials.

Rational functions are quotients of polynomials. Like polynomials, rational functions play a very important role in mathematics and the sciences. Just as with rational numbers, rational functions are usually expressed in "lowest terms." For a given numerator and denominator pair, this involves finding their greatest common divisor polynomial and removing it from both the numerator and denominator.

Sours: https://www.wolframalpha.com/calculators/factoring-calculator

## Simplification or other simple results

(2x2 + 6x) - 12

### Step  3  :

#### Pulling out like terms :

Pull out like factors :

2x2 + 6x - 12  =   2 • (x2 + 3x - 6)

#### Trying to factor by splitting the middle term

Factoring  x2 + 3x - 6

The first term is,  x2  its coefficient is  1 .
The middle term is,  +3x  its coefficient is  3 .
The last term, "the constant", is  -6

Step-1 : Multiply the coefficient of the first term by the constant   1 • -6 = -6

Step-2 : Find two factors of  -6  whose sum equals the coefficient of the middle term, which is   3 .

 -6 + 1 = -5 -3 + 2 = -1 -2 + 3 = 1 -1 + 6 = 5

Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored

### Final result :

2 • (x2 + 3x - 6)
Sours: https://www.tiger-algebra.com/drill/2x~2_6x/

## Simplification or other simple results

### Step  1  :

6x - 12 Simplify ——————— x2 - 4

### Step  2  :

#### Pulling out like terms :

Pull out like factors :

6x - 12  =   6 • (x - 2)

#### Trying to factor as a Difference of Squares :

Factoring:  x2 - 4

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2- AB + AB - B2 =
A2 - B2

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check : 4 is the square of 2
Check :  x2  is the square of  x1

Factorization is :       (x + 2)  •  (x - 2)

#### Canceling Out :

Cancel out  (x - 2)  which appears on both sides of the fraction line.

### Final result :

6 ————— x + 2
Sours: https://www.tiger-algebra.com/drill/(6x)/(x~)/

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## 12 factored 6x

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Factoring Common Monomial Factor

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### Now discussing:

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