Regents Exam: Algebra I August 2016 (Problem 23 of 37)

The video tutorial explains how to determine the possible factorization of a polynomial function by analyzing its graph. It introduces the concept of polynomial factorization, including prime polynomials, and demonstrates how to identify zeros or x-intercepts from a graph to construct the polynomial's factored form. An example is provided to illustrate these concepts, and the tutorial concludes by applying this knowledge to solve a specific problem, identifying the correct factorization from given options.

What is a polynomial called if it cannot be factored over the integers?

• Simple polynomial

• Composite polynomial

• Prime polynomial

• Complex polynomial

If a polynomial has a zero at x = -1, what is the corresponding factor?

• x - 1

• x + 1

• x + 2

• x - 2

How do the signs of the zeros change when writing the factors of a polynomial?

• They become negative

• They double

• They switch signs

• They remain the same

Given the zeros -3, 2, and 4, which of the following is a factor of the polynomial?

• x + 3

• x + 2

• x - 3

• x + 4

Which option correctly matches the factorization of the polynomial with zeros at -3, 2, and 4?

• (x - 3)(x + 2)(x + 4)

• (x + 3)(x - 2)(x - 4)

• (x + 3)(x + 2)(x - 4)

• (x - 3)(x - 2)(x + 4)