Given One Zero or Factor Find the Remaining Zeros

The video tutorial explains how to find all zeros of a polynomial given one zero using synthetic division. It covers setting up synthetic division, solving the polynomial, and factoring the resulting polynomial to find all zeros. The process involves using coefficients, applying the zero product property, and verifying results.

What is the first step in setting up synthetic division when given a zero?

• Add the zero to the polynomial

• Write the zero on the outside and align the coefficients

• Multiply the zero by the first coefficient

• Align the terms in descending order

What does a remainder of zero indicate in synthetic division?

• The zero is not a factor of the polynomial

• The polynomial is prime

• The zero is a factor of the polynomial

• The polynomial has no real zeros

How can you express the polynomial after performing synthetic division?

• As a difference of cubes

• As a single term

• As a product of factors

• As a sum of squares

Which method is used to find additional zeros after synthetic division?

• Graphing the polynomial

• Further factoring the polynomial

• Using the quadratic formula

• Completing the square

What is the zero product property used for in this context?

• To determine the leading coefficient

• To solve for the zeros of the polynomial

• To find the sum of the zeros

• To verify the degree of the polynomial