Find All the Zeros Using of a Polynomial to the 4th Power

The video tutorial explains how to find zeros of a polynomial using various methods, including the rational zero test and factoring. It highlights the limitations of the rational zero test and demonstrates factoring over rationals and reals. The tutorial concludes with a fully factored polynomial using linear factorization, emphasizing the importance of understanding different approaches to solving polynomial equations.

What is the first method mentioned for finding zeros of a polynomial?

• Graphing the polynomial

• Using synthetic division

• Factoring the polynomial

• Using the quadratic formula

What does the rational zero test help determine?

• The constant term of the polynomial

• The leading coefficient of the polynomial

• Possible rational zeros of the polynomial

• The degree of the polynomial

Why was the rational zero test not helpful in this case?

• The polynomial had no zeros

• The zeros were not rational

• The zeros were complex

• The polynomial was already factored

Which two numbers multiply to -27 and add to 6 in the factoring process?

• 27 and -1

• 3 and -9

• 9 and -3

• 6 and -27

What is the result of factoring the polynomial over the rationals?

• X - sqrt(3) * X + sqrt(3)

• X^2 + 9

• X^2 + 3

• X^2 - 3

What is the term used for the fully factored polynomial?

• Linear factorization

• Cubic factorization

• Polynomial division

• Quadratic factorization

What property allows setting each factor equal to zero to find the zeros?

• Commutative property

• Zero product property

• Distributive property

• Associative property