IBEW Polynomial Factoring Methods 3 — Questions and Answers
Question 1: Factor: 4x² - 25
- (2x - 5)(2x + 5) (Correct answer)
- (4x - 5)(x + 5)
- (2x - 25)(2x + 1)
- (4x + 5)(x - 5)
Correct answer: (2x - 5)(2x + 5)
4x² − 25 is a difference of squares: (2x)² − 5² = (2x − 5)(2x + 5).
Question 2: What is the GCF of 12x³, 18x², and 6x?
- 6x (Correct answer)
- 6x²
- 12x
- 3x
Correct answer: 6x
The GCF of 12, 18, and 6 is 6, and the lowest power of x is x¹, so GCF = 6x.
Question 3: Factor completely: x⁴ - 16
- (x² - 4)(x² + 4)
- (x² + 4)(x - 2)(x + 2)
- (x - 2)(x + 2)(x² + 4) (Correct answer)
- (x - 4)(x + 4)
Correct answer: (x - 2)(x + 2)(x² + 4)
x⁴ − 16 = (x² − 4)(x² + 4) = (x − 2)(x + 2)(x² + 4); x² + 4 cannot be factored further over integers.
Question 4: Factor: x² - x - 12
- (x - 4)(x + 3) (Correct answer)
- (x + 4)(x - 3)
- (x - 6)(x + 2)
- (x + 6)(x - 2)
Correct answer: (x - 4)(x + 3)
Find numbers multiplying to −12 and adding to −1: −4 and 3, giving (x − 4)(x + 3).
Question 5: If one factor of x² - 7x + 10 is (x - 2), what is the other factor?
- (x - 5) (Correct answer)
- (x + 5)
- (x - 10)
- (x + 2)
Correct answer: (x - 5)
Dividing x² − 7x + 10 by (x − 2) gives (x − 5), verified by −2 × −5 = 10 and −2 + −5 = −7.
Question 6: Factor: 6x² - 7x - 3
- (3x + 1)(2x - 3) (Correct answer)
- (2x - 3)(3x + 1)
- (6x + 1)(x - 3)
- (3x - 1)(2x + 3)
Correct answer: (3x + 1)(2x - 3)
AC method: 6×(−3)=−18; factors summing to −7 are −9 and 2; rewrite and group to get (3x + 1)(2x − 3).
Question 7: Factor: x² + 4x - 21
- (x + 7)(x - 3) (Correct answer)
- (x - 7)(x + 3)
- (x + 21)(x - 1)
- (x + 3)(x - 7)
Correct answer: (x + 7)(x - 3)
Find factors of −21 adding to 4: 7 and −3, giving (x + 7)(x − 3).
