Polynomial Degree and Roots Concepts

The video explains the fundamental theorem of algebra, which states that a polynomial of degree n has exactly n roots. It provides examples of linear, quadratic, and cubic polynomials, demonstrating how to find real and imaginary roots both analytically and graphically. The video emphasizes the importance of understanding the nature of roots and how they relate to the polynomial's degree.

What does the Fundamental Theorem of Algebra state about the roots of a polynomial?

• A polynomial of degree n has n-1 roots.

• A polynomial of degree n has n+1 roots.

• A polynomial of degree n has no roots.

• A polynomial of degree n has exactly n roots.

If a linear polynomial is set to zero, how many solutions does it have?

• Two solutions

• Infinite solutions

• No solutions

• One solution

What is the degree of the polynomial x^2 - 4, and how many roots does it have?

• Degree 2, one root

• Degree 1, one root

• Degree 2, two roots

• Degree 3, three roots

How can the polynomial x^2 - 4 be factored?

• (x + 2)(x + 2)

• (x - 2)(x - 2)

• (x - 2)(x + 2)

• (x - 4)(x + 4)

What type of roots does the polynomial x^2 + 4 have?

• Two real roots

• Two imaginary roots

• One real root

• No roots

How do imaginary roots appear in polynomials?

• In fours

• In pairs

• Singly

• In threes

What is the degree of the polynomial x^3 - 2x^2 + x - 2?

• Degree 3

• Degree 1

• Degree 2

• Degree 4

How many real roots does the polynomial x^3 - 2x^2 + x - 2 have?

• Two real roots

• Three real roots

• No real roots

• One real root

What method can be used to factor the polynomial x^3 - 2x^2 + x - 2?

• Synthetic division

• Grouping

• Quadratic formula

• Completing the square

What does the graph of the polynomial x^3 - 2x^2 + x - 2 indicate about its roots?

• It has no x-intercepts.

• It has two x-intercepts.

• It has one x-intercept.

• It has three x-intercepts.