Factorization

1. Factorization : Factorization is the process of expressing a polynomial as the product of two or more polynomials. It is the reverse process of expanding a polynomial.
2. Basic Factorization Formulas
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3. Factorization of Complex Expressions
1. Factorization of Polynomials with Common Parts
1. Substitute the common part as , and express the given polynomial in terms of .
2. Factorize.
3. Substitute the original expression back for and continue factorizing.
2. Factorization of Biquadratic Expressions
   A biquadratic expression consists of even powers of terms, such as , where and are constants. It can be factorized using two methods:
1. Substitute and factorize.
2. Separate the quadratic terms by focusing on the fourth and constant terms, then factorize in the form of .
3. Factorization of Expressions with Multiple Variables
1. Organize the expression in descending order with respect to the variable with the lowest degree. If all terms have the same degree, organize by one of the variables.
2. If there is a common factor, group it and factorize.
   If the constant term is long, first factorize the constant term, then factorize the entire expression.
4. Factorization Using the Factor Theorem
   A polynomial of degree three or higher can be factorized using the Factor Theorem and Synthetic Division as follows:
1. Find the value of that satisfies . If all coefficients of are integers, the possible values of are:
   
2. Use synthetic division to divide by , and obtain the quotient , then express as .
3. Repeat the process for the quotient .


Example 1 : Factorize the polynomial
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 Solution
If we let , then

Example 2 : When the polynomial is factored into , what is the value of for two positive integers and ?
 Solution