Master how to find all of the zeros of a polynomial when given two irrational zeros

The video tutorial explains how to find all zeros of a polynomial, focusing on rational zeros. It covers the use of synthetic division, factoring, and the difference of squares to simplify the process. The tutorial also discusses alternative methods, such as long division, to verify and find additional zeros. The importance of the fundamental theorem of algebra in determining the number of zeros is highlighted.

What is the first step in finding the zeros of a polynomial?

• Using long division

• Setting F(x) to zero

• Applying the zero product property

• Checking the degree of the polynomial

Which property is applied when multiplying terms in synthetic division?

• Associative property

• Distributive property

• Identity property

• Commutative property

What is the result of multiplying a term by its conjugate?

• Product of squares

• Quotient of squares

• Sum of squares

• Difference of squares

How can you verify the number of zeros in a polynomial?

• By factoring out common terms

• By using the zero product property

• By checking the degree of the polynomial

• By applying synthetic division

What is the zero product property used for?

• To divide polynomials

• To set factors equal to zero

• To multiply polynomials

• To find the degree of a polynomial

What is an alternative method to synthetic division for finding zeros?

• Using the Pythagorean theorem

• Applying the binomial theorem

• Rewriting zeros as factors

• Using the quadratic formula

When is long division necessary in polynomial factorization?

• When the polynomial has no real zeros

• When the polynomial is quadratic

• When synthetic division fails

• When the factor is to a power larger than one