What is the value of 0 factorial, and why is it significant in Pascal's Triangle?

Properties of Prime Numbers in Pascal's Triangle

Interactive Video
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Mathematics
•
9th - 10th Grade
•
Hard

Amelia Wright
FREE Resource
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Undefined, as factorials are not defined for zero
0, because it represents an empty set
1, because it maintains the structure of Pascal's Triangle
10, as a placeholder value
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How does the concept of factorials help in understanding Pascal's Triangle?
Factorials are not related to Pascal's Triangle
Factorials are used to compute binomial coefficients
Factorials help in understanding the symmetry of the triangle
Factorials are used to calculate the area of the triangle
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What unique property do rows in Pascal's Triangle that start with a prime number have?
They are symmetrical
All coefficients are divisible by the prime number
They have no unique properties
They contain only even numbers
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why are terms in non-prime rows of Pascal's Triangle not divisible by the row number?
Because the row number is always odd
Due to the cancellation of factors in the binomial coefficient
Because the row number is always even
Because the terms are always prime
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the main takeaway from the section on non-divisibility in non-prime rows?
Non-prime rows are always divisible by their row number
Non-prime rows have unique divisibility properties
Non-prime rows do not have terms divisible by the row number due to factor cancellation
Non-prime rows are symmetrical
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In Pascal's Triangle, why do rows corresponding to prime numbers have all terms divisible by the prime?
Because the triangle is symmetrical
Because the terms are always even
Because prime numbers cannot be canceled out in the binomial coefficient
Because prime numbers are always at the top of the triangle
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the significance of the prime number pattern in Pascal's Triangle?
It indicates that all numbers in the triangle are prime
It shows that all rows are symmetrical
It highlights the unique divisibility properties of prime rows
It suggests that the triangle is infinite
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