Factorizations example sentences

"Factorizations" Example Sentences

1. The teacher asked the students to write down all possible factorizations of the number 12.
2. She is quite good at finding unique factorizations of large integers.
3. The mathematician is renowned for his work on integer factorizations.
4. It is important to understand the concept of prime factorizations when dealing with fractions.
5. The contest asked participants to find the number of distinct factorizations of a given integer.
6. The textbook contains several examples of polynomial factorizations.
7. The professor asked the students to prove the unique factorization theorem.
8. One of the key applications of number theory is the study of prime factorizations.
9. The main task in solving this equation is to find the factorizations of the given expressions.
10. There are a few general techniques for determining the number of distinct factorizations of an integer.
11. The lecture focused on the applications of factorizations in cryptography.
12. In algebra, factorizations are used to simplify complex expressions.
13. The student found it difficult to understand the concept of unique factorizations.
14. The theorem on unique factorization of integers is a fundamental result in number theory.
15. The concept of factorizations can be used to find the roots of a polynomial equation.
16. The contest involved finding the number of prime factorizations for a given integer.
17. One of the interesting properties of unique factorizations is that they are unique up to order and units.
18. The lecture covered several methods for finding factorizations of polynomials over finite fields.
19. The textbook has several exercises on finding factorizations of large composite numbers.
20. Factorizations play a crucial role in the cryptographic algorithm used for secure communication.
21. The student was able to prove the fundamental theorem of arithmetic, which states that any integer can be expressed as a product of primes in a unique way, up to the order of factors.
22. The mathematician was able to find a new algorithm for computing factorizations of large integers.
23. The theorem on unique factorization states that any integer can be expressed as a product of primes in one and only one way.
24. The lecture covered various properties of factorizations, such as associativity and distributivity.
25. The student was able to derive the formula for the number of distinct factorizations of a given integer using combinatorics.
26. The contest required contestants to find all possible factorizations of a given polynomial over a given field.
27. The theorem on unique factorization is usually proved using induction on the number of prime factors.
28. The student was able to show that the number of distinct factorizations of an integer is equal to its divisor function.
29. The professor showed how factorizations can be used to solve Diophantine equations.
30. The lecture covered some recent developments in the study of factorizations, such as algebraic geometry and algebraic number theory.

Common Phrases

1. Finding prime factorizations;
2. Using prime factorizations to simplify fractions;
3. Factoring quadratic expressions;
4. Finding greatest common factor (GCF);
5. Factoring trinomials;
6. Factoring polynomials with multiple terms;
7. Factoring the sum or difference of cubes;
8. Decomposing a function into factors;
9. Factoring by grouping;
10. Factoring perfect square trinomials.