Bluebook SAT Test Equivalent Expressions 6 — Questions and Answers
Question 1: Which of the following is equivalent to 9x² − 30x + 25?
- (3x − 5)² (Correct answer)
- (9x − 5)(x − 5)
- (3x + 5)²
- (3x − 5)(3x + 5)
Correct answer: (3x − 5)²
9x² − 30x + 25 = (3x)² − 2(3x)(5) + 5² = (3x − 5)².
Question 2: Which expression is equivalent to (x² − 5x + 4)/(x − 1)?
- x + 4
- x − 4 (Correct answer)
- x² − 4
- x − 1
Correct answer: x − 4
Factor: x² − 5x + 4 = (x − 1)(x − 4); cancel (x − 1): result = x − 4.
Question 3: Which of the following is equivalent to (x^3)(x^−5)?
- x²
- x^−2 (Correct answer)
- x^15
- x^−8
Correct answer: x^−2
x³ · x⁻⁵ = x^(3 + (−5)) = x^(−2).
Question 4: Which of the following is equivalent to (3x)/(x − 2) + (6)/(x − 2)?
- (3x + 6)/(x − 2)
- 3(x + 2)/(x − 2) (Correct answer)
- 3
- 3(x + 2)/(2(x − 2))
Correct answer: 3(x + 2)/(x − 2)
(3x + 6)/(x − 2) = 3(x + 2)/(x − 2); this cannot be simplified further.
Question 5: Which of the following is equivalent to −2(x − 3)² + 18?
- −2x² + 12x
- −2x(x − 6) (Correct answer)
- −2x² + 12x + 18
- −2x(x + 6)
Correct answer: −2x(x − 6)
Expand: −2(x² − 6x + 9) + 18 = −2x² + 12x − 18 + 18 = −2x² + 12x = −2x(x − 6).
Question 6: Which of the following is equivalent to (4x² − 9)/(2x + 3)?
- 2x − 3 (Correct answer)
- 2x + 3
- 4x − 3
- 2x − 9
Correct answer: 2x − 3
4x² − 9 = (2x + 3)(2x − 3); cancel (2x + 3): result = 2x − 3.
Question 7: Which of the following is equivalent to (x + 3)/4 − (x − 1)/4?
- (2x + 2)/4
- 4/4 = 1
- 1 (Correct answer)
- x/2
Correct answer: 1
(x + 3 − (x − 1))/4 = (x + 3 − x + 1)/4 = 4/4 = 1.
Bluebook SAT Test Equivalent Expressions 6
Which of the following is equivalent to 9x² − 30x + 25?