# Factorization: Quiz

Question 1: Factoring integers is covered by the fundamental theorem of arithmetic and factoring polynomials by the ________.
Fundamental theorem of calculusGroup (mathematics)Fundamental theorem of algebraFundamental theorem of Galois theory

Question 2: Given an algorithm for integer factorization, one can factor any integer down to its constituent ________ by repeated application of this algorithm.
Deficient numberPractical numberPerfect numberPrime number

Question 3: where α and β are the two roots of the polynomial, found with the ________.

Question 4: In ________, factorization (also factorisation in British English) or factoring is the decomposition of an object (for example, a number, a polynomial, or a matrix) into a product of other objects, or factors, which when multiplied together give the original.
Set theoryMathematicsGeometryMathematical logic

Question 5: There are different types: ________, LQ, QL, RQ, RZ.
Matrix (mathematics)QR decompositionGram–Schmidt processSingular value decomposition

Question 6: By the ________, every positive integer has a unique prime factorization.
Fundamental theorem of arithmeticEuclidean algorithmPrime numberFundamental theorem of algebra

Question 7: Its complexity is the basis of the assumed security of some public key cryptography algorithms, such as ________.

Question 8: One major example of this uses an orthogonal or unitary matrix, and a ________.
Triangular matrixMatrix (mathematics)DeterminantDiagonalizable matrix

Question 9: ________ for large integers appears to be a difficult problem.
Euclidean algorithmSolovay–Strassen primality testInteger factorizationPrimality test

Question 10: Another example is the factorization of a function as the composition of other functions having certain properties; for example, every function can be viewed as the composition of a surjective function with an ________.
Inverse functionConstructivism (mathematics)BijectionInjective function