Understanding Prime Numbers and Polynomial Functions

What is a prime number?

• A number that is odd

• A number that is even

• A number divisible by 2 and 3

• A number divisible by 1 and itself only

What is a Mersenne prime?

• A prime number of the form n^2 - 1

• A prime number of the form 2^n + 1

• A prime number of the form n^2 + 1

• A prime number of the form 2^n - 1

Which mathematician is associated with Fermat primes?

• Pierre de Fermat

• Leonhard Euler

• Carl Friedrich Gauss

• Isaac Newton

What is the form of a Fermat prime?

• 2^(2^n) + 1

• 2^n - 1

• n^2 - 1

• n^2 + 1

What is the polynomial f(x) = x^2 - x + 41 known for?

• Generating composite numbers for the first 40 values of x

• Generating odd numbers for all values of x

• Generating even numbers for all values of x

• Generating prime numbers for the first 40 values of x

What happens when x = 41 in the polynomial f(x) = x^2 - x + 41?

• The result is not a prime number

• The result is a prime number

• The result is an even number

• The result is an odd number

What is the significance of the polynomial f(x) = x^2 - 79x + 61?

• It generates composite numbers for the first 80 values of x

• It generates odd numbers for all values of x

• It generates even numbers for all values of x

• It generates prime numbers for the first 80 values of x

Why can't a polynomial generate prime numbers for all integer values?

• Because it would only produce even numbers

• Because it would eventually produce composite numbers

• Because it would only produce negative numbers

• Because it would only produce odd numbers

What is the degree of a polynomial?

• The highest power of x in the polynomial

• The lowest power of x in the polynomial

• The sum of all coefficients

• The number of terms in the polynomial

What does the fundamental theorem of algebra imply about polynomials?

• A polynomial of degree n cannot take the same value more than n times

• A polynomial can generate prime numbers for all values of x

• A polynomial can only have even coefficients

• A polynomial can only have odd coefficients