IBEW Aptitude Test Polynomial Factoring Methods Questions and Answers 2 — Questions and Answers

Question 1: Factor: x² - 16

(x - 4)(x + 4) (Correct answer)
(x - 8)(x + 2)
(x - 4)²
(x + 16)(x - 1)

Correct answer: (x - 4)(x + 4)

Difference of squares: x² - 4² = (x-4)(x+4).

Difference of squares: a² - b² = (a-b)(a+b). x² - 16 = x² - 4². Let a=x, b=4. Factored: (x-4)(x+4). Verify: (x-4)(x+4) = x² + 4x - 4x - 16 = x² - 16 ✓. This is one of the most commonly tested factoring patterns.

Question 2: What are the roots of x² - 5x + 6 = 0?

x = 1 and x = 6
x = 2 and x = 3 (Correct answer)
x = −2 and x = −3
x = −1 and x = −6

Correct answer: x = 2 and x = 3

Factor: (x-2)(x-3) = 0. So x = 2 or x = 3.

x² - 5x + 6 = 0. Factor: find two numbers with product=6, sum=-5: -2 and -3. (x-2)(x-3)=0. Set each factor to zero: x-2=0 → x=2; x-3=0 → x=3. Roots are x=2 and x=3. Finding roots by factoring is a key quadratic skill on IBEW aptitude tests.

Question 3: Factor by grouping: x³ + 2x² + 3x + 6

(x + 2)(x² + 3) (Correct answer)
(x + 3)(x² + 2)
(x² + 2)(x + 3)
(x + 1)(x² + 6)

Correct answer: (x + 2)(x² + 3)

Group: (x³+2x²) + (3x+6). Factor each: x²(x+2) + 3(x+2). Factor out (x+2): (x+2)(x²+3).

Step 1: Group: (x³+2x²)+(3x+6). Step 2: Factor each group: x²(x+2) + 3(x+2). Step 3: Both groups have factor (x+2): (x+2)(x²+3). Verify: x³+3x+2x²+6 = x³+2x²+3x+6 ✓. Factoring by grouping applies to 4-term polynomials.

Question 4: Which is a perfect square trinomial?

x² + 4x + 3
x² + 6x + 9 (Correct answer)
x² - 5x + 4
x² + 8x + 12

Correct answer: x² + 6x + 9

x² + 6x + 9 = (x+3)². Check: 2×1×3=6 (middle term), 3²=9 (constant). Perfect square.

Perfect square trinomial form: a² + 2ab + b² = (a+b)². For x²+6x+9: a=x, b=3. 2ab=2(x)(3)=6x ✓, b²=9 ✓. So x²+6x+9=(x+3)². The other options don't fit this pattern. Recognizing perfect square trinomials speeds up factoring on timed aptitude tests.

Question 5: Factor completely: 2x³ - 8x

2x(x-2)(x+2) (Correct answer)
x(2x-8)
2(x³-4x)
2x(x²-8)

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

Factor out 2x: 2x(x²-4). Factor difference of squares: 2x(x-2)(x+2).

Step 1: GCF = 2x. Factor: 2x(x²-4). Step 2: x²-4 is difference of squares: (x-2)(x+2). Complete: 2x(x-2)(x+2). Multi-step factoring (GCF + difference of squares) is a common IBEW aptitude test question type. Always factor completely.

Question 6: Expand: (3x - 2)(3x + 2)

9x² - 4 (Correct answer)
9x² + 4
9x² - 12x + 4
6x² - 4

Correct answer: 9x² - 4

Difference of squares: (a-b)(a+b) = a² - b². (3x-2)(3x+2) = 9x² - 4.

(3x-2)(3x+2) uses the identity (a-b)(a+b) = a² - b². a=3x, b=2. (3x)² = 9x², 2² = 4. Result: 9x² - 4. The middle terms cancel (−6x + 6x = 0). Knowing this pattern allows instant expansion without full FOIL.

IBEW Aptitude Test Polynomial Factoring Methods Questions and Answers 2

Factor: x² - 16