Given One Zero or Factor Find the Remaining Zeros

The video tutorial explains how to find the remaining zeros of a polynomial when given a complex zero. It covers two methods: using the complex conjugate and long division. The instructor provides a step-by-step example, demonstrating the importance of considering both positive and negative roots when dealing with complex numbers. The tutorial emphasizes the use of long division over synthetic division for polynomials of higher degrees and concludes with a summary of the process.

What must be considered when dealing with complex zeros?

• Only the positive value

• Only the negative value

• Both positive and negative values

• Neither positive nor negative values

Why can't synthetic division be used with quadratic factors?

• It requires a polynomial of the second degree

• It is too complex for quadratic factors

• It is only applicable to linear equations

• It requires a binomial of the first power

What is the first step in performing long division on a polynomial?

• Divide the leading term of the dividend by the leading term of the divisor

• Subtract the divisor from the dividend

• Multiply the divisor by the dividend

• Add the divisor to the dividend

What is the result of dividing X^3 + X^2 + 9X + 9 by X^2 + 9?

• X^2 + 9

• X - 9

• X + 9

• X^3 + 9

What is the final zero found after completing the division?

• 9

• -1

• -3i

• 3i