Factorization Practice Test Quiz

Approved & Edited by ProProfs Editorial Team

The editorial team at ProProfs Quizzes consists of a select group of subject experts, trivia writers, and quiz masters who have authored over 10,000 quizzes taken by more than 100 million users. This team includes our in-house seasoned quiz moderators and subject matter experts. Our editorial experts, spread across the world, are rigorously trained using our comprehensive guidelines to ensure that you receive the highest quality quizzes.

Learn about Our Editorial Process

| By Gregorynaomi

Gregorynaomi

Community Contributor

Quizzes Created: 1462 | Total Attempts: 825,507

Questions: 10 | Attempts: 813 | Updated: Mar 19, 2023

Questions

Settings

Feedback

During the Quiz End of Quiz

Difficulty

Sequential Easy First Hard First

Play as

Quiz Flashcard

Create your own Quiz

Share on Facebook Share on Twitter Share on Whatsapp Share on Pinterest Share on Email Copy to Clipboard Embed on your website

When it comes to factorization in mathematics, we look for multiples of a number as well other numbers that can divide the variable perfectly. Put, factorization involves expressing a number as a product of two or more numbers. Do you know arithmetic? Have you mastered factorization? Get tested on factorization now!

Questions and Answers

1.

Which of these is not a factor of 15?
- A.
  
  3
- B.
  
  5
- C.
  
  1
- D.
  
  10
Correct Answer
D. 10

Explanation
The number 10 is not a factor of 15 because a factor of a number is a whole number that can be divided evenly into that number. When we divide 15 by 10, we get a remainder of 5, which means 10 is not a factor of 15.

Rate this question:
2.

Which of these is not a multiple of 15?
- A.
  
  15
- B.
  
  60
- C.
  
  45
- D.
  
  100
Correct Answer
D. 100

Explanation
The number 100 is not a multiple of 15 because it cannot be divided evenly by 15. A multiple of a number is obtained by multiplying that number by any whole number. In this case, 15 multiplied by 1 gives 15, 15 multiplied by 2 gives 30, and so on. However, when we multiply 15 by any whole number, we will never get 100 as the result. Therefore, 100 is not a multiple of 15.

Rate this question:

0
1
3.

Which of these is a method for factorizing quadratic equations?
- A.
  
  Dividing the square
- B.
  
  Completing the square
- C.
  
  Multiplying the square
- D.
  
  Subtracting the square
Correct Answer
B. Completing the square

Explanation
Completing the square is a method for factorizing quadratic equations. This involves manipulating the equation to create a perfect square trinomial, which can then be factored easily. By adding or subtracting a constant term to both sides of the equation, the quadratic expression can be expressed as the square of a binomial, allowing for easy factorization. This method is commonly used when solving quadratic equations or simplifying expressions involving quadratic terms.

Rate this question:
4.

What formula is used in factorizing quadratic equations?
- A.
  
  General formula
- B.
  
  Communitative formula
- C.
  
  Polynomial formula
- D.
  
  Quadratic formula
Correct Answer
D. Quadratic formula

Explanation
The quadratic formula is used to factorize quadratic equations. It is derived from completing the square method and can be used to find the roots or solutions of a quadratic equation. The formula is x = (-b ± √(b^2 - 4ac)) / 2a, where a, b, and c are the coefficients of the quadratic equation. By substituting the values of a, b, and c into the formula and simplifying, the roots of the equation can be determined.

Rate this question:
5.

What are integral domains which share similar property after factorization called?
- A.
  
  Tagged domain
- B.
  
  Divisor domain
- C.
  
  Independent domain
- D.
  
  General domain
Correct Answer
B. Divisor domain

Explanation
Divisor domain is the correct answer because integral domains that share a similar property after factorization are called divisor domains. In a divisor domain, every nonzero element can be factored into irreducible elements, and this factorization is unique up to associates. This property allows for the cancellation of common factors in a divisor domain, making it a useful concept in algebraic number theory and commutative algebra.

Rate this question:
6.

Which of these factors of 45 is not a prime number?
- A.
  
  3
- B.
  
  15
- C.
  
  5
- D.
  
  1
Correct Answer
B. 15

Explanation
The number 15 is not a prime number because it is divisible by both 3 and 5. A prime number is a number that is only divisible by 1 and itself, but 15 can be divided by other numbers as well. Therefore, 15 is not a prime factor of 45.

Rate this question:
7.

Which of these domain is euclidean when factorized?
- A.
  
  Divisor domain
- B.
  
  Integral domain
- C.
  
  Ideal domain
- D.
  
  Principal domain
Correct Answer
B. Integral domain

Explanation
An integral domain is a commutative ring in which the product of any two non-zero elements is non-zero. When a domain is factorized, it means that it can be expressed as a product of irreducible elements. In an integral domain, every element can be factored in a unique way into irreducible elements, similar to prime factorization in the integers. Therefore, an integral domain is euclidean when factorized.

Rate this question:
8.

How many factors of 90 are less than 10?
- A.
  
  2
- B.
  
  6
- C.
  
  12
- D.
  
  4
Correct Answer
B. 6

Explanation
The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90. Out of these, the factors that are less than 10 are 1, 2, 3, 5, 6, and 9. Therefore, there are 6 factors of 90 that are less than 10.

Rate this question:
9.

How many factors of 20 are prime numbers?
- A.
  
  3
- B.
  
  7
- C.
  
  5
- D.
  
  10
Correct Answer
A. 3

Explanation
There are 3 prime factors of 20. The prime factors of 20 are 2, 2, and 5.

Rate this question:
10.

What is the highest factor of 8?
- A.
  
  1
- B.
  
  3
- C.
  
  2
- D.
  
  4
Correct Answer
D. 4

Explanation
The highest factor of 8 is 4 because a factor is a number that divides evenly into another number. In this case, 4 is the largest number that can divide evenly into 8 without leaving a remainder.

Rate this question:

1
0