MindMap Gallery Factorization techniques
There are various factors that require selecting appropriate methods based on the characteristics of polynomials. Proficiency in these techniques can help simplify the operation and analysis of polynomials. If you need it, please collect it now!
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Factorization techniques
Promotional factor method
Extract the maximum common factor
Determine the common factors of each item
Decompose the greatest common factor
Grouping decomposition method
Group polynomials
Each group extracts the common factors separately
Check whether it can be further decomposed
Formula Method
Difference square formula
a^2 b^2 = (a b)(a b)
Complete square formula
a^2 2ab b^2 = (a b)^2
a^2 2ab b^2 = (a b)^2
Cross multiplication formula
a^2 b^2 = (a b)(a b)
How to match
Convert quadratic polynomials to fully squared form
Apply the fully squared formula
Decomposition of cross multiplication
Applicable to binomial multiplied by trinomial
Find a combination of equal products of coefficients and constant terms
Check the symbol of the middle item
High-order polynomial decomposition
Grouping method
Group higher order polynomials
Factorization is performed within each group
Synthesis division
Used to find the root of a polynomial
Decompose a polynomial into a factorial product by root
Long-term division method
Used to simplify polynomials
Gradually reduce the number of times the polynomial
Special polynomial decomposition
Symmetric polynomial
Decomposition using symmetric properties
Circular polynomial
Decomposition using the properties of cyclic permutation
Binomial theorem
Factorization using binomial expansion
Application of factorization
Solve equations
Convert equations into a form where the product of the factor equals zero
Simplify expressions
Simplify complex expressions into easier to process
Solve practical problems
Apply factorization to solve practical problems