IBEW Aptitude Test Polynomials and Factoring Questions and Answers 2 — Questions and Answers

Question 1: Factor: x² - 9

(x - 3)(x + 3) (Correct answer)
(x - 9)(x + 1)
(x - 3)²
(x + 9)(x - 1)

Correct answer: (x - 3)(x + 3)

x² - 9 is a difference of squares: a² - b² = (a-b)(a+b). Here a=x, b=3. So (x-3)(x+3).

The difference of squares pattern: a² - b² = (a - b)(a + b). For x² - 9 = x² - 3²: a=x, b=3. Factored: (x-3)(x+3). This is one of the most important factoring patterns and appears regularly on the IBEW NJATC aptitude test.

Question 2: Expand: (x + 4)(x + 3)

x² + 7x + 7
x² + 7x + 12 (Correct answer)
x² + 12x + 7
x² + 8x + 12

Correct answer: x² + 7x + 12

FOIL: x·x + x·3 + 4·x + 4·3 = x² + 3x + 4x + 12 = x² + 7x + 12.

FOIL method for (x+4)(x+3): First: x×x=x², Outer: x×3=3x, Inner: 4×x=4x, Last: 4×3=12. Combine: x² + (3x+4x) + 12 = x² + 7x + 12. Expanding binomials using FOIL is a standard algebra skill tested on IBEW aptitude exams.

Question 3: Factor: 6x² + 9x

3x(2x + 3) (Correct answer)
6x(x + 3)
3(2x² + 3x)
2x(3x + 9)

Correct answer: 3x(2x + 3)

GCF of 6x² and 9x is 3x. Factor out: 3x(2x + 3).

6x² = 2 × 3 × x × x, 9x = 3 × 3 × x. GCF = 3x. Dividing: 6x²/3x = 2x, 9x/3x = 3. Factored form: 3x(2x + 3). Factoring by GCF is the first step in any factoring problem and is extensively tested on aptitude exams.

Question 4: What is the degree of the polynomial 4x³ - 2x² + 7x - 1?

1
2
3 (Correct answer)
4

Correct answer: 3

The degree is the highest power of x, which is 3 (from 4x³).

The degree of a polynomial is determined by its highest-degree term. In 4x³ - 2x² + 7x - 1, the terms have degrees 3, 2, 1, and 0. The highest is 3, so this is a cubic polynomial (degree 3). Understanding polynomial terminology is tested on IBEW aptitude exams.

Question 5: Factor: x² + 5x + 6

(x + 1)(x + 6)
(x + 2)(x + 3) (Correct answer)
(x + 6)(x - 1)
(x - 2)(x - 3)

Correct answer: (x + 2)(x + 3)

Find two numbers that multiply to 6 and add to 5: 2 and 3. Factored: (x+2)(x+3).

For x² + bx + c, find two numbers with product=c and sum=b. Here b=5, c=6. Numbers: 2 and 3 (2×3=6, 2+3=5). Factored: (x+2)(x+3). Verify: x²+3x+2x+6 = x²+5x+6 ✓. This trinomial factoring method is a core IBEW aptitude test skill.

Question 6: Simplify: (2x² + 4x) / (2x)

x + 1
x + 2 (Correct answer)
2x + 2
x² + 2

Correct answer: x + 2

Factor numerator: 2x(x + 2). Divide by 2x: (x + 2).

Numerator: 2x² + 4x = 2x(x + 2). Dividing by 2x: 2x(x+2)/2x = x + 2. Simplifying rational expressions by factoring and canceling is a key algebra skill tested on the IBEW NJATC aptitude exam.

IBEW Aptitude Test Polynomials and Factoring Questions and Answers 2

Factor: x² - 9