IBEW Polynomial Factoring Methods 5 — Questions and Answers
Question 1: Factor: x³ + 8
- (x + 2)(x² - 2x + 4) (Correct answer)
- (x - 2)(x² + 2x + 4)
- (x + 2)(x² + 2x + 4)
- (x + 2)³
Correct answer: (x + 2)(x² - 2x + 4)
Sum of cubes: x³ + 2³ = (x + 2)(x² − 2x + 4) using a³ + b³ = (a + b)(a² − ab + b²).
Question 2: Factor: 4x² + 12x + 9
- (2x + 3)² (Correct answer)
- (4x + 3)(x + 3)
- (2x + 9)(2x + 1)
- (2x - 3)²
Correct answer: (2x + 3)²
4x² + 12x + 9 = (2x)² + 2(2x)(3) + 3² = (2x + 3)², a perfect square trinomial.
Question 3: Which is the fully factored form of 2x³ - 8x?
- 2x(x - 2)(x + 2) (Correct answer)
- 2x(x² - 4)
- 2(x³ - 4x)
- x(2x - 4)(x + 2)
Correct answer: 2x(x - 2)(x + 2)
Factor out 2x: 2x(x² − 4), then factor the difference of squares: 2x(x − 2)(x + 2).
Question 4: Factor: 3x² + 10x - 8
- (3x - 2)(x + 4) (Correct answer)
- (3x + 2)(x - 4)
- (x + 2)(3x - 4)
- (3x + 4)(x - 2)
Correct answer: (3x - 2)(x + 4)
AC method: 3×(−8)=−24; factors summing to 10 are 12 and −2; grouping gives (3x − 2)(x + 4).
Question 5: What technique is most efficient for factoring x⁶ - 64?
- Difference of squares applied twice (Correct answer)
- Grouping
- AC method
- Sum of cubes
Correct answer: Difference of squares applied twice
x⁶ − 64 = (x³)² − 8² = (x³ − 8)(x³ + 8), then each cubic can be factored further.
Question 6: Factor: x² - 2x - 48
- (x - 8)(x + 6) (Correct answer)
- (x + 8)(x - 6)
- (x - 12)(x + 4)
- (x + 12)(x - 4)
Correct answer: (x - 8)(x + 6)
Find factors of −48 adding to −2: −8 and 6, giving (x − 8)(x + 6).
Question 7: After factoring out the GCF from 15x²y - 10xy², what remains inside the parentheses?
- 3x - 2y (Correct answer)
- 3xy - 2y
- 3x - 2xy
- 15x - 10y
Correct answer: 3x - 2y
GCF of 15x²y and 10xy² is 5xy; dividing each term gives 3x − 2y inside the parentheses.
