Free IBEW Aptitude Test Polynomials and Factoring Questions and Answers 1 — 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?
- t = 2 and t = 6
- t = 1 and t = 3 (Correct answer)
- t = 1 and t = 9
- t = 3 and t = 4
Correct answer: t = 1 and t = 3
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)?
- 2x² + 4x - 6
- 4x² + 8x - 3
- 2x² + 4x - 3 (Correct answer)
- 2x³ + 4x² - 3x
Correct answer: 2x² + 4x - 3
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?
- 2x + 3
- x - 1
- 2x - 1
- 2x + 1 (Correct answer)
Correct answer: 2x + 1
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)?
- 6y² - 7y - 20
- 6y² + 23y - 20
- 6y² + 7y - 20 (Correct answer)
- 5y + 1
Correct answer: 6y² + 7y - 20
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?
- 8x
- 2x³ - 4x²
- -8x (Correct answer)
- 16
Correct answer: -8x
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).
Question 6: Which of the following is the greatest common factor (GCF) of the terms in the polynomial 12a³b² - 18a²b³ + 30a⁴b?
- 6a²b (Correct answer)
- 6a⁴b³
- 12a²b
- 6ab
Correct answer: 6a²b
To find the GCF, find the greatest common factor for the coefficients and for each variable. For the coefficients 12, 18, and 30, the GCF is 6. For the variable 'a' (a³, a², a⁴), the lowest power is a², so the GCF is a². For the variable 'b' (b², b³, b), the lowest power is b. Combining these gives the GCF of the entire polynomial: 6a²b.
Free IBEW Aptitude Test Polynomials and Factoring Questions and Answers 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?