Understanding Polynomial and Composite Numbers

What is unique about the polynomial n^4 - 20n^2 + 4?

• It generates only composite numbers.

• It generates only even numbers.

• It generates only prime numbers.

• It generates both prime and composite numbers.

How can you construct a polynomial that always outputs composite numbers?

• By multiplying the polynomial by a prime number.

• By adding a constant to the polynomial.

• By subtracting a constant from the polynomial.

• By squaring the polynomial and adding a multiple of a number.

What is a composite number in the context of this video?

• An integer that is always negative.

• An integer divisible only by 1 and itself.

• An integer divisible by numbers other than 1 and itself.

• An integer that is always positive.

Why is the polynomial n^4 - 20n^2 + 4 not a perfect square?

• Because it has an odd degree.

• Because it cannot be expressed as a square of a binomial.

• Because it has a non-zero constant term.

• Because it has a negative constant.

What method is used to factor the polynomial n^4 - 20n^2 + 4?

• Completing the square.

• Using the quadratic formula.

• Difference of squares.

• Synthetic division.

What must be proven to show that the polynomial always outputs composite numbers?

• That the polynomial is a perfect square.

• That neither factor is plus or minus one.

• That the polynomial is always positive.

• That the polynomial is always negative.

What happens if one of the factors of the polynomial equals plus or minus one?

• The polynomial becomes zero.

• The polynomial is no longer composite.

• The polynomial becomes a perfect square.

• The polynomial becomes a prime number.

What is the result of applying the quadratic formula to the factor n^2 - 4n - 3?

• It results in no solutions.

• It results in complex solutions.

• It results in non-integer solutions.

• It results in integer solutions.

Why can't the factor n^2 + 4n - 1 be equal to -1?

• Because it would make n a positive number.

• Because it would make n a negative number.

• Because it would make n a complex number.

• Because it would make n a non-integer.

What is the significance of proving that neither factor is plus or minus one?

• It shows the polynomial is always positive.

• It shows the polynomial is a prime number.

• It shows the polynomial is a perfect square.

• It shows the polynomial always outputs composite numbers.