FREE IBEW Aptitude Test Polynomials and Factoring Questions and Answers

Question 1

An electrical engineer models the voltage (V) in a circuit over time (t) using the polynomial V(t) = 3t² - 12t + 9. At which of the following times is the voltage equal to zero?

Accepted Answer

t = 1 and t = 3

Answer

To find when the voltage is zero, set the polynomial V(t) = 3t² - 12t + 9 equal to zero and solve for t. First, factor out the greatest common factor, which is 3, resulting in 3(t² - 4t + 3) = 0. Then, factor the quadratic expression inside the parentheses: t² - 4t + 3 factors to (t - 1)(t - 3). So, the equation becomes 3(t - 1)(t - 3) = 0. The values of t that make this equation true are t = 1 and t = 3.

Question 2

Which of the following expressions is the result of simplifying (4x³ + 8x² - 6x) / (2x)?

Accepted Answer

2x² + 4x - 3

Answer

To simplify the expression, divide each term of the polynomial in the numerator by the monomial in the denominator. (4x³ / 2x) + (8x² / 2x) - (6x / 2x). This simplifies to 2x² + 4x - 3.

Question 3

The area of a rectangular electrical panel is given by the polynomial 2x² + 7x + 3. If the width of the panel is (x + 3), what is the length?

Accepted Answer

2x + 1

Answer

The area of a rectangle is length times width. To find the length, you must factor the area polynomial 2x² + 7x + 3. Factoring this trinomial results in (2x + 1)(x + 3). Since the width is given as (x + 3), the length must be the other factor, which is (2x + 1).

Question 4

What is the product of the binomials (3y - 4) and (2y + 5)?

Accepted Answer

6y² + 7y - 20

Answer

To find the product, use the FOIL method (First, Outer, Inner, Last). First: (3y)(2y) = 6y². Outer: (3y)(5) = 15y. Inner: (-4)(2y) = -8y. Last: (-4)(5) = -20. Combine the like terms (15y - 8y = 7y) to get the final expression: 6y² + 7y - 20.

Question 5

A signal processing function is described by the polynomial P(x) = (x² + 4)(x - 2) - (x² - 4)(x + 2). Which of the following is the simplified form of this polynomial?

Accepted Answer

-8x

Answer

To factor the polynomial 8x³ - 18x completely, first identify the greatest common factor (GCF) of the terms. The GCF of 8x³ and 18x is 2x. Factoring out 2x gives 2x(4x² - 9). The expression inside the parentheses, 4x² - 9, is a difference of squares, which can be factored as (2x - 3)(2x + 3). Therefore, the complete factorization is 2x(2x - 3)(2x + 3).

IBEW - Aptitude Test Practice Test

IBEW - Aptitude Test Practice Test

FREE IBEW Aptitude Test Polynomials and Factoring Questions and Answers