Bluebook SAT Test Equivalent Expressions 7 — Questions and Answers
Question 1: Which of the following is equivalent to 2x² + 5x − 3?
- (2x − 1)(x + 3) (Correct answer)
- (2x + 1)(x − 3)
- (x + 3)(2x − 1)
- (2x + 3)(x − 1)
Correct answer: (2x − 1)(x + 3)
(2x − 1)(x + 3) = 2x² + 6x − x − 3 = 2x² + 5x − 3 ✓.
Question 2: Which of the following is equivalent to ((x²y)/(z))²?
- x⁴y²/z
- x⁴y²/z² (Correct answer)
- x²y²/z²
- 2x²y/z²
Correct answer: x⁴y²/z²
Apply the power to each part: (x²)² = x⁴, y² = y², z² = z²; result = x⁴y²/z².
Question 3: Which of the following is equivalent to (2x − 1)/(3) + (x + 2)/(3)?
- (3x + 1)/3 (Correct answer)
- x + 1
- (3x − 1)/3
- (x + 1)/3
Correct answer: (3x + 1)/3
Add numerators over common denominator: (2x − 1 + x + 2)/3 = (3x + 1)/3.
Question 4: Which of the following is equivalent to (x² − 2x − 8)?
- (x − 4)(x + 2) (Correct answer)
- (x + 4)(x − 2)
- (x − 4)(x − 2)
- (x + 4)(x + 2)
Correct answer: (x − 4)(x + 2)
Find two numbers that multiply to −8 and add to −2: −4 and +2; so (x − 4)(x + 2).
Question 5: Which of the following is equivalent to a⁰ for any nonzero value of a?
- 0
- a
- 1 (Correct answer)
- −1
Correct answer: 1
Any nonzero number raised to the power 0 equals 1, by definition of the zero exponent rule.
Question 6: Which of the following is equivalent to (6x³ − 4x² + 2x)/(2x)?
- 3x² − 2x + 1 (Correct answer)
- 3x² − 4x + 2
- 6x² − 4x + 2
- 3x³ − 2x²
Correct answer: 3x² − 2x + 1
Divide each term: 6x³/2x − 4x²/2x + 2x/2x = 3x² − 2x + 1.
Question 7: Which of the following is equivalent to (x − 5)(x + 5) − x(x − 10)?
- 10x − 25 (Correct answer)
- x² − 25
- 25 − 10x
- −25
Correct answer: 10x − 25
(x² − 25) − x(x − 10) = x² − 25 − x² + 10x = 10x − 25.
Bluebook SAT Test Equivalent Expressions 7
Which of the following is equivalent to 2x² + 5x − 3?