IBEW Polynomial Factoring Methods 4 — Questions and Answers
Question 1: Factor the sum of cubes: 8x³ + 27
- (2x + 3)(4x² - 6x + 9) (Correct answer)
- (2x - 3)(4x² + 6x + 9)
- (2x + 3)(4x² + 6x + 9)
- (2x + 3)³
Correct answer: (2x + 3)(4x² - 6x + 9)
Using a³ + b³ = (a + b)(a² − ab + b²) with a = 2x and b = 3: (2x + 3)(4x² − 6x + 9).
Question 2: Which polynomial CANNOT be factored over integers?
- x² + 9 (Correct answer)
- x² - 9
- x² + x - 6
- x² - 5x + 6
Correct answer: x² + 9
x² + 9 is a sum of squares, which cannot be factored over the integers.
Question 3: Factor by grouping: 2ax + 2ay + bx + by
- (2a + b)(x + y) (Correct answer)
- (a + b)(2x + y)
- (2a + b)(x + 2y)
- (a + 2b)(x + y)
Correct answer: (2a + b)(x + y)
Group as (2ax + 2ay) + (bx + by) = 2a(x + y) + b(x + y) = (2a + b)(x + y).
Question 4: What value of c makes x² + 8x + c a perfect square trinomial?
- 16 (Correct answer)
- 8
- 4
- 64
Correct answer: 16
For a perfect square, c = (8/2)² = 4² = 16, giving (x + 4)².
Question 5: Factor completely: 5x³ - 45x
- 5x(x - 3)(x + 3) (Correct answer)
- 5x(x² - 9)
- 5(x³ - 9x)
- x(5x - 15)(x + 3)
Correct answer: 5x(x - 3)(x + 3)
Factor out 5x to get 5x(x² − 9), then factor the difference of squares: 5x(x − 3)(x + 3).
Question 6: Factor: 9x² - 30x + 25
- (3x - 5)² (Correct answer)
- (3x + 5)²
- (9x - 5)(x - 5)
- (3x - 5)(3x + 5)
Correct answer: (3x - 5)²
9x² − 30x + 25 = (3x)² − 2(3x)(5) + 5² = (3x − 5)², a perfect square trinomial.
Question 7: Factor: x² - 14x + 49
- (x - 7)² (Correct answer)
- (x + 7)²
- (x - 49)(x - 1)
- (x - 7)(x + 7)
Correct answer: (x - 7)²
x² − 14x + 49 = (x − 7)² since 7² = 49 and 2(7) = 14.
IBEW Polynomial Factoring Methods 4
Factor the sum of cubes: 8x³ + 27