Rational Zero Theorem and Polynomial Zeros

The video tutorial covers the Rational Zero Theorem, explaining how to find possible rational zeros of polynomials using factors of the constant term and leading coefficient. It demonstrates the use of synthetic division to test these zeros and solve polynomials. The tutorial also discusses the Fundamental Theorem of Algebra, highlighting the relationship between polynomial degree and the number of solutions. Advanced factoring techniques are explored, emphasizing the importance of using known methods before resorting to the Rational Root Theorem.

What is the primary purpose of the Rational Zero Theorem?

• To calculate the derivative of a polynomial

• To determine all possible rational zeros of a polynomial

• To find the degree of a polynomial

• To integrate a polynomial

What is synthetic division used for in polynomial solving?

• To find the integral of a polynomial

• To calculate the derivative of a polynomial

• To determine the degree of a polynomial

• To prove that a number is a zero of a polynomial

Which of the following is NOT a step in using the Rational Zero Theorem?

• Finding factors of the constant term

• Finding factors of the leading coefficient

• Dividing each factor of the constant by each factor of the leading coefficient

• Calculating the derivative of the polynomial

What is the next step after finding possible rational zeros using the Rational Zero Theorem?

• Graphing the polynomial

• Finding the derivative of the polynomial

• Calculating the integral of the polynomial

• Performing synthetic division to test each possible zero

According to the Fundamental Theorem of Algebra, how many zeros does a polynomial of degree 5 have?

• 3

• 4

• 6

• 5

What is the first step in factoring a polynomial using the Rational Zero Theorem?

• Graphing the polynomial

• Finding the derivative

• Identifying the constant term and leading coefficient

• Calculating the integral