Tool to factorize a math expression. Factorization of a mathematical expression consists in expressing it as a product, it is the inverse of an expansion.
Math Expression Factorization - dCode
Tag(s) : Symbolic Computation
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Math Expression Factorization
Answers to Questions (FAQ)
What is factorization? (Definition)
Factorizing is the action of transforming a sum (an addition) into a product (a multiplication) of 2 factors (or more).
Example: The addition $ 3 x + 6 $ can be factorized as the multiplication $ 3 \times (x + 2) $
Factorization is a mathematical transformation modifying the writing of an expression without changing the result.
Factorization is the inverse transformation of expansion which consists of transforming a product into a sum
How to factorize a polynomial-like expression?
Several methods of factorization exist in mathematics:
Factorization by finding a common factor
Example: The addition $ 3a + 3b $ has two terms ($ 3a $ and $ 3b $) that have the common factor $ 3 $, so $ 3a+3b = 3(a+b) $
Factorization by identifying a remarkable identity
The most common outstanding identities allowing factorization are: $$ a^2 + 2ab + b^2 = (a+b)^2 \\ a^2 - 2ab + b^2 = (a-b)^2 \\ a^2 - b^2 = (a+b)(a-b) \\ 1-a^{n}=(1-a)(1+a+a^{2}+ \cdots +a^{n-1}) $$
Example: The expression $ x^2+2x+1 $ contains a remarkable identity of the form $ a^2 + 2ab + b^2 $ (with $ a = x $ and $ b = 1 $) so it can be factorized $ x^2+2x+1 = (x+1)^2 $
Factorization with polynomial roots
By knowing (or calculating) all the roots $ \alpha_i $ of a polynomial of variable $ x $, then this one can be factorized as the product of the $ (x-\alpha_i) $
Example: The polynomial $ x^2 - 2 $ has roots $ x = \sqrt{2} $ and $ x = -\sqrt{2} $ so it is factorized $ (x-\sqrt{2})(x+\sqrt{2}) $
What is integer factorization?
Factorization can also be applied to whole numbers, in order to determine if they are multiples of other numbers.
Example: $ 8 $ can be factorized $ 2 \times 4 $ or $ 4 \times 2 $ or $ 2 \times 2 \times 2 $
If an integer has no factors other than 1 and itself then it is a prime number.
The process of factoring an integer is also called prime number decomposition.
How to factorize a trigonometric expression?
dCode factorizes trigonometric expression in order to simplify them by expressing them with sin and cos
Example: $$ 1+1/\sec(x) = 2\cos(x/2)^2 $$
Example: $$ \cos(x+y) + \sin(x)\sin(y) = \cos(x)\cos(y) $$
How to display steps by steps?
The solver/factorizer has no real steps, at least not steps similar to those required of college or high school. For the moment steps are not displayed, but the solver allows checking a result.
Source code
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Math Expression Factorization on dCode.fr [online website], retrieved on 2024-12-21,
