Quadratic Expressions and Prime Numbers

The video tutorial explores whether the expression n^2 + n + 5 results in a prime number for any whole number value of N. Ali hypothesizes that it always results in a prime number. The teacher demonstrates the process of substituting values for N, showing calculations for N=1, 2, 3, and 4. While the first three values yield prime numbers, N=4 results in 25, which is not prime. This disproves Ali's hypothesis. The tutorial emphasizes the importance of reasoning and evaluation in mathematical problem-solving, explaining how to earn marks by showing calculations and conclusions.

What does Ali believe about the expression n^2 + n + 5?

• It will always be a prime number for any whole number value of N.

• It will always be an even number.

• It will always be a square number.

• It will always be a multiple of 5.

What is the result of the expression when N equals 2?

• 17

• 13

• 11

• 7

Which value of N results in a non-prime number for the expression?

• 4

• 2

• 3

• 1

What is the value of the expression when N equals 4?

• 16

• 30

• 25

• 20

Why is the expression not always prime for whole number values of N?

• Because it can result in a square number.

• Because it is always a multiple of 3.

• Because it is always even.

• Because it is always odd.