sarah786 said:Can you please explain how to factorize x4+2x2+9
If i do it by quadratic formula, i get complex roots ... in my book, it has been factorized to
(x2+2x+3)(x2-2x + 3)
sarah786 said:Can you please explain how to factorize x4+2x2+9
If i do it by quadratic formula, i get complex roots ... in my book, it has been factorized to
(x2+2x+3)(x2-2x + 3)
Let u=x2. Then you need to solve u2 +2u +9, and take square roots of both solutions.sarah786 said:Can you please explain how to factorize x4+2x2+9
If i do it by quadratic formula, i get complex roots ... in my book, it has been factorized to
(x2+2x+3)(x2-2x + 3)
Factorization is the process of breaking down a mathematical expression or number into smaller parts, called factors, that when multiplied together give the original expression or number. It is an important concept in algebra and can be used to simplify complex expressions and solve equations.
To factorize a polynomial, you need to find the common factors of all its terms and then use the distributive property to rewrite the expression as a product of these factors. This process can involve techniques such as factoring by grouping, finding the greatest common factor, and using the difference of squares or perfect square trinomial formulas.
Factorization is important because it allows us to rewrite complex expressions or numbers in a simpler form, making it easier to understand and work with them. It also plays a crucial role in solving equations and finding the roots of polynomial functions.
Sure, let's say we have the polynomial expression 2x^2 + 10x. The common factor here is 2x, so we can rewrite it as 2x(x + 5). This is an example of factoring by finding the greatest common factor. We can then use the distributive property to simplify it further to 2x^2 + 10x = 2x(x + 5) = 2x^2 + 10x.
Factorization has many real-world applications, such as in cryptography, where it is used to break down large numbers into their prime factors to make them more secure. It is also used in finance and economics to calculate interest rates and analyze financial data. In chemistry, factorization is used to balance chemical equations. Additionally, factorization is used in computer science for tasks such as data compression and error correction.