Math Math Algebra and Functions 2 — Questions and Answers
Question 1: Factor the expression x² − 9.
- (x + 3)(x − 3) (Correct answer)
- (x + 9)(x − 1)
- (x − 3)²
- (x + 3)²
Correct answer: (x + 3)(x − 3)
x² − 9 is a difference of squares: (x + 3)(x − 3).
Question 2: If f(x) = 2x + 5, what is f(−3)?
- -1 (Correct answer)
- 11
- 1
- -11
Correct answer: -1
f(−3) = 2(−3) + 5 = −6 + 5 = −1.
Question 3: Solve the system: x + y = 8 and x − y = 2.
- x = 5, y = 3 (Correct answer)
- x = 3, y = 5
- x = 6, y = 2
- x = 4, y = 4
Correct answer: x = 5, y = 3
Adding equations: 2x = 10, x = 5; then y = 8 − 5 = 3.
Question 4: What is the y-intercept of the line 3x + 2y = 12?
- 6 (Correct answer)
- 4
- 3
- 12
Correct answer: 6
Set x = 0: 2y = 12, y = 6, so the y-intercept is 6.
Question 5: Simplify: 3x² + 5x − 2x² + x
- x² + 6x (Correct answer)
- x² + 4x
- 5x² + 6x
- x² − 6x
Correct answer: x² + 6x
Combine like terms: (3x² − 2x²) + (5x + x) = x² + 6x.
Question 6: Which of the following is a solution to x² − 5x + 6 = 0?
- x = 2 (Correct answer)
- x = 1
- x = 4
- x = 5
Correct answer: x = 2
x² − 5x + 6 = (x − 2)(x − 3) = 0, giving solutions x = 2 or x = 3.
Math Math Algebra and Functions 2
Factor the expression x² − 9.