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

The video tutorial explains how to identify all zeros of a polynomial when given two complex zeros. It covers the use of synthetic division to find remaining zeros, discusses the importance of complex conjugates, and demonstrates how to factor polynomials to find real zeros. The tutorial also presents an alternative method using long division to achieve the same results, providing a comprehensive understanding of polynomial division and zero identification.

What does the fundamental theorem of algebra state about the number of zeros a polynomial has?

• A polynomial has as many zeros as its degree.

• A polynomial has twice as many zeros as its degree.

• A polynomial has half as many zeros as its degree.

• A polynomial has no relation to the number of zeros.

What is the purpose of using synthetic division in the context of finding zeros?

• To calculate the sum of all zeros.

• To find additional zeros when some zeros are already known.

• To determine the leading coefficient.

• To find the degree of the polynomial.

When using synthetic division, what is the significance of the remainder being zero?

• It suggests the polynomial has no real zeros.

• It means the polynomial is irreducible.

• It confirms that the divisor is a factor of the polynomial.

• It indicates a mistake in calculation.

How can the conjugate of a complex zero be used in finding other zeros?

• It can be ignored as it has no significance.

• It is used to find the polynomial's leading coefficient.

• It provides another zero of the polynomial.

• It helps in determining the polynomial's degree.

What is the advantage of using long division over synthetic division in some cases?

• Long division is faster and more efficient.

• Long division is the only method to find real zeros.

• Long division can handle polynomials with complex coefficients more easily.

• Long division provides a visual representation of the division process.

What is the result of multiplying two complex conjugate factors?

• A polynomial with only one zero.

• A polynomial with no coefficients.

• A polynomial with real coefficients.

• A polynomial with imaginary coefficients.

What are the zeros of the polynomial discussed in the tutorial?

• 3, 2, -2i, 2i

• 3, -2, 2i, -2i

• -3, 2, 2i, -2i

• -3, -2, 2i, 2i