Factorization Challenge
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Questions and Answers

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?

<p>No, except for rational numbers or functions (B)</p> Signup and view all the answers

Who first considered factorization?

<p>Ancient Greek mathematicians (C)</p> Signup and view all the answers

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

<p>Writing it in lowest terms and separately factoring its numerator and denominator (D)</p> Signup and view all the answers

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

<p>$(xy) imes (1/y)$ (D)</p> Signup and view all the answers

What does the fundamental theorem of arithmetic assert?

<p>Every integer can be factored into prime numbers (D)</p> Signup and view all the answers

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

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

What is a factorization of a mathematical object?

<p>Writing it as a product of several factors (A)</p> Signup and view all the answers

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