Bluebook SAT Test Equivalent Expressions 5 — Questions and Answers
Question 1: Which of the following is equivalent to (x² − 4x − 21)/(x − 7)?
- x + 3 (Correct answer)
- x − 3
- x + 7
- x − 7
Correct answer: x + 3
Factor: x² − 4x − 21 = (x − 7)(x + 3); cancel (x − 7): result = x + 3.
Question 2: Which of the following is equivalent to 12x²y³ − 8xy²?
- 4xy²(3xy − 2) (Correct answer)
- 4xy(3xy² − 2y)
- 4x²y²(3y − 2)
- 2xy²(6xy − 4)
Correct answer: 4xy²(3xy − 2)
GCF = 4xy²; 12x²y³/4xy² = 3xy, 8xy²/4xy² = 2; so 4xy²(3xy − 2).
Question 3: Which of the following is equivalent to (x + y)² − (x − y)²?
- 4xy (Correct answer)
- 2x²
- 2y²
- 4x²
Correct answer: 4xy
(x² + 2xy + y²) − (x² − 2xy + y²) = 4xy.
Question 4: Which of the following is equivalent to (x² + 4)/(x + 2)?
- x + 2
- x − 2 + 8/(x + 2) (Correct answer)
- x − 2
- x + 2 − 8/(x + 2)
Correct answer: x − 2 + 8/(x + 2)
Polynomial long division: x² + 4 ÷ (x + 2) = x − 2 remainder 8, giving x − 2 + 8/(x + 2).
Question 5: Which expression is equivalent to 3x(x − 2) + 4(x − 2)?
- (3x + 4)(x − 2) (Correct answer)
- (3x − 4)(x + 2)
- 3x² + 4x − 2
- (3x + 4)(x + 2)
Correct answer: (3x + 4)(x − 2)
Factor out (x − 2): 3x(x − 2) + 4(x − 2) = (3x + 4)(x − 2).
Question 6: Which of the following is equivalent to (2x/(x+1)) − (3/(x+1))?
- (2x − 3)/(x + 1) (Correct answer)
- (2x − 3)/(2x + 2)
- −1/(x + 1)
- (2x + 3)/(x + 1)
Correct answer: (2x − 3)/(x + 1)
Same denominator: (2x − 3)/(x + 1).
Question 7: Which of the following is equivalent to (x^4 − 16)/(x² − 4)?
- x² + 4 (Correct answer)
- x² − 4
- x² + 2x + 4
- x + 2
Correct answer: x² + 4
x⁴ − 16 = (x² + 4)(x² − 4); cancel (x² − 4): result = x² + 4.
Bluebook SAT Test Equivalent Expressions 5
Which of the following is equivalent to (x² − 4x − 21)/(x − 7)?