IBEW Polynomial Factoring Methods 2 — Questions and Answers
Question 1: Factor the trinomial: x² + 11x + 30
- (x + 5)(x + 6)
- (x + 3)(x + 10) (Correct answer)
- (x + 2)(x + 15)
- (x + 6)(x + 5)
Correct answer: (x + 3)(x + 10)
Find two numbers that multiply to 30 and add to 11: 3 and 10, giving (x + 3)(x + 10).
Question 2: Which expression is a perfect square trinomial?
- x² + 6x + 9 (Correct answer)
- x² + 6x + 8
- x² + 5x + 9
- x² + 4x + 9
Correct answer: x² + 6x + 9
x² + 6x + 9 = (x + 3)² because the middle term equals 2 times the square root of the last term times x.
Question 3: Factor completely: 3x² - 12
- 3(x - 2)(x + 2) (Correct answer)
- 3(x² - 4)
- (3x - 6)(x + 2)
- 3(x - 4)(x + 1)
Correct answer: 3(x - 2)(x + 2)
Factor out 3 to get 3(x² − 4), then factor the difference of squares to get 3(x − 2)(x + 2).
Question 4: What are the factors of x² - 10x + 25?
- (x - 5)² (Correct answer)
- (x + 5)²
- (x - 5)(x + 5)
- (x - 25)(x - 1)
Correct answer: (x - 5)²
x² − 10x + 25 is a perfect square trinomial equal to (x − 5)².
Question 5: Factor: 2x² + 5x + 3
- (2x + 3)(x + 1) (Correct answer)
- (2x + 1)(x + 3)
- (x + 1)(2x + 3)
- (x + 3)(2x + 1)
Correct answer: (2x + 3)(x + 1)
Using the AC method: 2×3=6; factors of 6 summing to 5 are 2 and 3, giving (2x + 3)(x + 1).
Question 6: Which method is best for factoring x³ - 27?
- Difference of cubes (Correct answer)
- Difference of squares
- Grouping
- Trinomial method
Correct answer: Difference of cubes
x³ − 27 = x³ − 3³ is a difference of cubes, factored as (x − 3)(x² + 3x + 9).
Question 7: Factor by grouping: x³ + 2x² + 3x + 6
- (x² + 3)(x + 2) (Correct answer)
- (x + 2)(x² + 3)
- (x + 3)(x² + 2)
- (x² + 2)(x + 3)
Correct answer: (x² + 3)(x + 2)
Group as (x³ + 2x²) + (3x + 6) = x²(x + 2) + 3(x + 2) = (x² + 3)(x + 2).
IBEW Polynomial Factoring Methods 2
Factor the trinomial: x² + 11x + 30