IBEW Aptitude Test Polynomial Factoring Methods Questions and Answers

Question 1

An electrical calculation results in the polynomial 4x² - 49. Which of the following represents the correct factored form of this expression?

Accepted Answer

(2x + 7)(2x - 7)

Answer

(4x - 7)(x + 7)

Answer

(2x - 7)²

Answer

This polynomial cannot be factored.

Question 2

Which of the following expressions is the result of fully factoring 3x³ + 6x² - 9x?

Accepted Answer

3x(x + 3)(x - 1)

Answer

3x(x² + 2x - 3)

Answer

3(x³ + 2x² - 3x)

Answer

x(3x + 9)(x - 1)

Question 3

A signal processing equation is given by the polynomial 2x² - 5x - 12. What is its factored form?

Accepted Answer

(2x + 3)(x - 4)

Answer

(2x - 4)(x + 3)

Answer

(2x - 6)(x + 2)

Answer

(x + 4)(2x - 3)

Question 4

Factor the polynomial 9x² - 24x + 16 completely.

Accepted Answer

(3x - 4)²

Answer

(9x - 4)(x - 4)

Answer

(3x + 4)(3x - 4)

Answer

(3x - 8)(3x - 2)

Question 5

An apprentice is trying to simplify the expression x³ - 4x² + 5x - 20. Which factoring method is most appropriate to start with for this polynomial?

Accepted Answer

Factoring by Grouping

Answer

Difference of Squares

Answer

Greatest Common Factor

Answer

Perfect Square Trinomial

Question 6

To solve for a variable in a circuit, you need to factor the expression n² + 8n - 48. What is the correct factored form?

Accepted Answer

(n - 4)(n + 12)

Answer

(n + 6)(n - 8)

Answer

(n - 6)(n + 8)

Answer

(n + 4)(n - 12)