Factorization Challenge

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What is the factorization of the integer 15?

$5 / 3$

$3 - 5$

$3 imes 5$ (correct)

$3 + 5$

What is the factorization of the polynomial $x^2 - 4$?

$(x + 2)^2$

$(x - 2)(x + 2)$ (correct)

$(x - 2)^2$

$(x - 2)(x - 2)$

What does factorization consist of?

Writing a number as a difference of factors

Writing a number as a product of factors (correct)

Writing a number as a sum of factors

Writing a number as a quotient of factors

Is factorization considered meaningful within number systems possessing division?

No, except for rational numbers or functions Signup and view all the answers

Who first considered factorization?

Ancient Greek mathematicians Signup and view all the answers

What is a meaningful factorization for a rational number or a rational function?

Writing it in lowest terms and separately factoring its numerator and denominator Signup and view all the answers

What can any non-zero $x$ be trivially written as, within number systems possessing division?

$(xy) imes (1/y)$ Signup and view all the answers

What does the fundamental theorem of arithmetic assert?

Every integer can be factored into prime numbers Signup and view all the answers

Why is factorization not usually considered meaningful within number systems possessing division?

Because any $x$ can be trivially written as $(xy) imes (1/y)$ whenever $y$ is not zero Signup and view all the answers

What is a factorization of a mathematical object?

Writing it as a product of several factors Signup and view all the answers

Factorization Challenge

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Questions and Answers

What is the factorization of the integer 15?

What is the factorization of the polynomial $x^2 - 4$?

What does factorization consist of?

Is factorization considered meaningful within number systems possessing division?

Who first considered factorization?

What is a meaningful factorization for a rational number or a rational function?

What can any non-zero $x$ be trivially written as, within number systems possessing division?

What does the fundamental theorem of arithmetic assert?

Why is factorization not usually considered meaningful within number systems possessing division?

What is a factorization of a mathematical object?

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