How to Find All of the Zeros Including Complex When Given a Polynomial

The video tutorial covers finding zeros of a polynomial using various methods. It starts with the fundamental theorem of algebra, explaining the possible combinations of real and complex zeros. The instructor then discusses sign changes to determine real zeros and introduces the rational zero test. Synthetic division is used to find zeros, and the quadratic formula is applied to find complex zeros. The tutorial emphasizes understanding the process and using tools like graphing calculators to verify results.

According to the fundamental theorem of algebra, how many zeros should a polynomial of degree 4 have?

• 5

• 2

• 3

• 4

What does Descartes' Rule of Signs help determine in a polynomial function?

• The degree of the polynomial

• The leading coefficient

• The number of positive and negative real zeros

• The sum of the coefficients

What is the purpose of the Rational Root Theorem in polynomial functions?

• To find the maximum value

• To calculate the derivative

• To determine the possible rational zeros

• To find the degree of the polynomial

Which method can be used to verify potential zeros of a polynomial?

• Long division

• Synthetic division

• Differentiation

• Integration

What is the factor of a polynomial if 1 is a zero?

• X + 2

• X - 1

• X + 1

• X - 2

When a quadratic equation is non-factorable, which method is used to find its zeros?

• Rational Root Theorem

• Long division

• Quadratic formula

• Synthetic division

How are complex solutions expressed when using the quadratic formula?

• As imaginary numbers

• As a combination of real and imaginary parts

• As whole numbers

• As real numbers