EDPT Algebraic Concepts and Equations 3 — Questions and Answers
Question 1: Factor the expression x² - 9 completely.
- (x - 3)²
- (x + 3)(x - 3) (Correct answer)
- (x - 9)(x + 1)
- (x + 9)(x - 1)
Correct answer: (x + 3)(x - 3)
x² - 9 is a difference of squares, factoring as (x + 3)(x - 3).
Question 2: If 5 - 2x > 11, which of the following must be true?
- x > -3
- x < -3 (Correct answer)
- x > 3
- x < 3
Correct answer: x < -3
Subtract 5 from both sides: -2x > 6; dividing by -2 (flip sign) gives x < -3.
Question 3: What is the solution to the system: x + y = 7 and x - y = 3?
- x = 2, y = 5
- x = 5, y = 2 (Correct answer)
- x = 4, y = 3
- x = 3, y = 4
Correct answer: x = 5, y = 2
Adding both equations gives 2x = 10, so x = 5; substituting gives y = 2.
Question 4: Which value of x satisfies x² = 81?
- x = 9 only
- x = -9 only
- x = 9 or x = -9 (Correct answer)
- x = 40.5
Correct answer: x = 9 or x = -9
Both 9² = 81 and (-9)² = 81, so x = ±9.
Question 5: Simplify: (3x²)(4x³)
- 7x⁵
- 12x⁶
- 12x⁵ (Correct answer)
- 7x⁶
Correct answer: 12x⁵
Multiply coefficients (3 × 4 = 12) and add exponents (2 + 3 = 5) to get 12x⁵.
Question 6: If a train travels at rate r mph for t hours, which expression gives the distance traveled?
- r + t
- r / t
- r × t (Correct answer)
- r - t
Correct answer: r × t
Distance = rate × time, so distance = r × t.
Question 7: What is the y-intercept of the equation 3x - 2y = 12?
- y = 4
- y = -6 (Correct answer)
- y = 6
- y = -4
Correct answer: y = -6
Set x = 0: -2y = 12, so y = -6.
EDPT Algebraic Concepts and Equations 3
Factor the expression x² - 9 completely.