Finding All of the Zeros of a Polynomial Including Complex

The video tutorial covers the process of identifying factors of a polynomial, using the remainder and factor theorems to check for factors, and applying the quadratic formula for non-factorable polynomials. It also explains Descartes' rule of signs to determine the number of positive and negative real zeros in a polynomial.

What is the first step in finding the zeros of a polynomial without a calculator?

• Apply Descartes' Rule of Signs

• Use the quadratic formula

• Begin with positive 1 and negative 1

• Start with the largest factor

Which theorem helps determine if a number is a zero of a polynomial?

• Fundamental Theorem of Algebra

• Remainder Theorem

• Pythagorean Theorem

• Binomial Theorem

What is the result when a polynomial is divided by one of its factors?

• A remainder of 0

• A negative remainder

• An undefined result

• A remainder of 1

What method is used when a polynomial is not factorable?

• Synthetic division

• Long division

• Graphical method

• Quadratic formula

How many complex solutions are there if a polynomial is not factorable?

• Three

• Two

• None

• One

What does Descartes' Rule of Signs help determine?

• The constant term

• The leading coefficient

• The number of real zeros

• The degree of the polynomial

According to Descartes' Rule of Signs, what indicates the number of positive real zeros?

• The number of terms in the polynomial

• The number of sign changes in the polynomial

• The sum of the coefficients

• The degree of the polynomial