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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