Factorization Practice Test Quiz

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1/10 Questions

Which of these is not a factor of 15?
- 3
- 5
- 1
- 10

About This Quiz

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!

2.

Which of these is not a multiple of 15?
- 15
- 60
- 45
- 100
Correct Answer

A. 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.

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3.

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

A. 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.

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4.

What formula is used in factorizing quadratic equations?
- General formula
- Communitative formula
- Polynomial formula
- Quadratic formula
Correct Answer

A. 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.

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5.

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

A. 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.

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6.

Which of these factors of 45 is not a prime number?
- 3
- 15
- 5
- 1
Correct Answer

A. 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.

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7.

Which of these domain is euclidean when factorized?
- Divisor domain
- Integral domain
- Ideal domain
- Principal domain
Correct Answer

A. 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.

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8.

How many factors of 90 are less than 10?
- 2
- 6
- 12
- 4
Correct Answer

A. 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.

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9.

How many factors of 20 are prime numbers?
- 3
- 7
- 5
- 10
Correct Answer

A. 3

Explanation

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

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10.

What is the highest factor of 8?
- 1
- 3
- 2
- 4
Correct Answer

A. 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.

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