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Factor Calculation Quiz

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Questions and Answers

What is the first step in finding the total number of factors of $73^{3} - 40^{3} - 33^{3}$?

Find the prime factorization of the expression $73^{3} - 40^{3} - 33^{3}$

Factor the expression $73^{3} - 40^{3} - 33^{3}$ using the difference of cubes formula (correct)

Calculate the value of the expression $73^{3} - 40^{3} - 33^{3}$

Determine the greatest common factor of 73, 40, and 33

Which of the following is the correct factorization of the expression $73^{3} - 40^{3} - 33^{3}$ using the difference of cubes formula?

(73 - 40 - 33)(73^{2} + 40^{2} + 33^{2})

(73 - 40 - 33)(73^{2} + 73 * 40 + 40^{2} + 73 * 33 + 40 * 33 + 33^{2})

(73 - 40)(73^{2} + 73 * 40 + 40^{2}) - (33)(33^{2})

(73 - 40)(73^{2} + 73 * 40 + 40^{2}) - (33 - 40)(33^{2} + 33 * 40 + 40^{2}) (correct)

What is the prime factorization of the expression $73^{3} - 40^{3} - 33^{3}$?

2^3 * 3 * 5 * 7 * 11^2 * 13

2^3 * 3 * 5^2 * 11 * 13 * 19

2^3 * 3 * 5 * 11 * 79

2^3 * 3 * 5 * 11 * 13 * 79 (correct)

How is the total number of factors of an integer calculated using its prime factorization?

<p>Add 1 to each exponent in the prime factorization and then multiply the results. (A)</p> Signup and view all the answers

What is the total number of factors of $73^{3} - 40^{3} - 33^{3}$?

<p>36 (C)</p> Signup and view all the answers

Flashcards

Difference of Cubes

A formula to factor expressions of the form a^3 - b^3.

Calculate 73^3 - 40^3 - 33^3

Determine the value of the expression using the difference of cubes.

Finding Total Number of Factors

The total count of positive integers that divide a number evenly without a remainder.

Prime Factorization

Expressing a number as a product of its prime numbers.

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Options for the Answer

Given choices to select the total number of factors: 16, 96, 120, 36.

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Study Notes