Given One Zero or Factor Find the Remaining Zeros

The video tutorial explains how to find all zeros of a polynomial when given a radical root. It begins by introducing the concept of zeros and the problem setup. The instructor then demonstrates using the square root property to find zeros, emphasizing the importance of considering both positive and negative roots. Next, synthetic division is used to verify the zeros, showing how it divides the polynomial evenly. Finally, the tutorial covers factoring polynomials and using conjugate pairs to find linear factors, concluding with the identification of all zeros using the Zero Product Property.

What is the significance of zeros in a polynomial function?

• They are roots, solutions, and X-intercepts.

• They represent the highest degree of the polynomial.

• They are only solutions to the equation.

• They determine the polynomial's leading coefficient.

When given a square root as a zero, what must you consider?

• Only the negative square root.

• Both positive and negative square roots.

• Only the positive square root.

• The square root of the polynomial's degree.

What is the purpose of using synthetic division in this context?

• To determine the polynomial's end behavior.

• To calculate the polynomial's leading coefficient.

• To verify if a given number is a zero.

• To find the degree of the polynomial.

What is the result when a zero divides a polynomial evenly?

• The remainder is non-zero.

• The polynomial's degree increases.

• The remainder is zero.

• The polynomial becomes linear.

What is the role of conjugate pairs in finding polynomial factors?

• They determine the polynomial's leading term.

• They help find linear factors.

• They increase the polynomial's roots.

• They simplify the polynomial's degree.

Which of the following is a factor of the polynomial given in the tutorial?

• X + sqrt 2

• X + 3

• X - 2

• X - sqrt 3

Using the Zero Product Property, what are the zeros of the polynomial?

• 2, -2, -sqrt 3

• -2, -sqrt 3, sqrt 3

• -2, 2, sqrt 3

• 2, sqrt 3, -sqrt 3