Understanding Polynomial Bounds and Zeros

What is the condition for a value to be considered an upper bound for the real zeros of a polynomial function?

• The K value is less than zero.

• The polynomial has no real zeros.

• All numbers in the last line of synthetic division are negative.

• All numbers in the last line of synthetic division are non-negative.

In the example given, what is the upper bound for the real zeros of the polynomial function?

• 9

• 7

• 5

• 3

What does it mean if the numbers in the last line of synthetic division alternate between non-negative and non-positive?

• The K value is an upper bound.

• The K value is a lower bound.

• The polynomial has no zeros.

• The polynomial is undefined.

Which theorem is used to identify potential real zeros of a polynomial function?

• Binomial Theorem

• Rational Zero Theorem

• Fundamental Theorem of Algebra

• Intermediate Value Theorem

What are the P values derived from in the Rational Zero Theorem?

• The sum of coefficients

• The degree of the polynomial

• The constant term

• The leading coefficient

After narrowing down the list of potential zeros, which value was confirmed as a zero using synthetic division?

• x = 2

• x = 4

• x = 0

• x = -1

What factor corresponds to the zero x = 4?

• x + 4

• 2x + 1

• 2x - 1

• x - 4

What is the next zero found after x = 4 using synthetic division?

• x = 1/2

• x = -1/2

• x = 3/2

• x = -3/2

What is the remaining factor of the polynomial after finding the zeros x = 4 and x = -1/2?

• 2x^2 - 4

• x^2 - 4

• x^2 + 4

• 2x^2 + 4

What are the final zeros of the polynomial function?

• x = ±√3

• x = ±1

• x = ±√2

• x = ±2