# Finding Zeros of a Polynomial Given One Complex Zero

Taught by mrbrianmclogan
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Lesson Summary:

In this lesson, we learn how to find the rest of the zeros of a polynomial when given one complex zero. By knowing that complex zeros come in conjugate pairs, we can use synthetic division to produce the rest of the factors or zeros. We treat our complex numbers like x's and add and multiply accordingly. By doing this, we can find the remaining zeros and factors of the polynomial.

Lesson Description:

Given one complex zero find the remaining zeros of a polynomial

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• How can I do synthetic division with an imaginary number?
• If I know one imaginary root of a cubic polynomial, how can I find the other two roots?
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The instructor shows how to use synthetic division, with an imaginary root, to find the remaining roots of a cubic polynomial.