Overview of rational Zeros of a polynomial- Online Math Tutor

The video tutorial provides an overview of rational roots in polynomials, discussing key theorems like the Fundamental Theorem of Algebra and the Linear Factorization Theorem. It explains the concept of polynomial roots, both real and imaginary, and introduces methods to find these roots, including factoring and the Rational Zero Test. The tutorial also covers the use of synthetic division and graphing calculators to identify potential rational zeros.

What does the fundamental theorem of algebra state about the roots of a polynomial?

• A polynomial has only imaginary roots.

• A polynomial has no roots.

• A polynomial has at least one root in the complex number system.

• A polynomial has only real roots.

According to the linear factorization theorem, what is the maximum number of zeros a polynomial can have?

• Equal to the highest degree of the polynomial.

• Equal to the number of terms in the polynomial.

• Always three.

• Always one.

What is a common method to start finding the zeros of a polynomial?

• Using imaginary numbers.

• Factoring the polynomial.

• Completing the square.

• Using the quadratic formula.

What is the rational zero test used for?

• To find all real zeros of a polynomial.

• To find all imaginary zeros of a polynomial.

• To find all possible rational zeros of a polynomial.

• To find the degree of a polynomial.

Which of the following is NOT a method to verify rational roots?

• Using evaluation.

• Using the quadratic formula.

• Using a graphing calculator.

• Using synthetic division.

What indicates that a number is a root when using synthetic division?

• A remainder of zero.

• A positive remainder.

• A remainder of one.

• A negative remainder.

How can you confirm a number is a root using evaluation?

• If the function value is one.

• If the function value is zero.

• If the function value is negative.

• If the function value is positive.