**Factoring**

When a polynomial is represented as a product of two or more polynomials, the polynomial is divided into factors. Factoring is useful when dealing with polynomials. Often, it is even necessary to find a solution.

### Factoring a number

When a number is divided by its factors, it is presented as the product of prime numbers.

### Factoring a polynomial

**Example 1**

The common factor

Divide the polynomial by its factors by using the common factor

Both terms have a common factor of *4x*, so taking it as a common factor leaves *x + 2* to be the factor inside parentheses.

**Example 2**

The square of a binomial

Divide the polynomial by its factors by forming the square of a binomial

**Example 3**

The product of the sum and the subtract

Divide the polynomial by its factors by forming the product of the sum and the subtract

**Example 4**

Grouping

Divide the polynomial by its factors using grouping. That is, the terms are grouped so that common factors are appropriately obtained.

Move the terms of the second and first degree to obtain the common factors* x* and *2*. Take the expression in parentheses as a common factor. At the end we have the product of the sum and the subtract.

**Example 5**

Using zeros

A polynomial can always be divided into its factors by its zeros.

For example, it is true for a quadratic polynomial that

We use zeros for factoring

Substitute into the formula

A polynomial factorized using its zeros

**Example 6**

Simplify the fraction

The numerator and denominator must be in product form so that we can reduce the fraction. We divide them both into their factors. The numerator has the common factor and the denominator is the product of the sum and the subtract

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