Bluebook SAT Test Nonlinear Equations and Systems 3 — Questions and Answers
Question 1: Which of the following is equivalent to x² − 16?
- (x − 4)(x + 4) (Correct answer)
- (x − 8)(x + 2)
- (x − 4)²
- (x + 4)²
Correct answer: (x − 4)(x + 4)
x² − 16 is a difference of squares: (x−4)(x+4).
Question 2: What is the positive solution of 3x² − 27 = 0?
- x = 3 (Correct answer)
- x = 6
- x = 9
- x = √3
Correct answer: x = 3
3x² = 27 → x² = 9 → x = ±3; the positive solution is x = 3.
Question 3: If (x − 3)² = 25, what are the possible values of x?
- x = 8 only
- x = −2 only
- x = 8 or x = −2 (Correct answer)
- x = 3 ± 25
Correct answer: x = 8 or x = −2
x − 3 = ±5 → x = 8 or x = −2.
Question 4: Which quadratic has roots at x = −1 and x = 5?
- x² − 4x − 5 (Correct answer)
- x² + 4x − 5
- x² − 4x + 5
- x² + 4x + 5
Correct answer: x² − 4x − 5
Using factor form: (x+1)(x−5) = x² − 4x − 5.
Question 5: How many real solutions does x² + 4 = 0 have?
- None (Correct answer)
- One
- Two
- Four
Correct answer: None
x² = −4 has no real solutions since a square cannot be negative.
Question 6: The product of two consecutive even integers is 48. Which equation models this situation?
- n² + 2n − 48 = 0 (Correct answer)
- n² − 2n − 48 = 0
- n² + 2n + 48 = 0
- 2n² − 48 = 0
Correct answer: n² + 2n − 48 = 0
Let the smaller even integer be n; n(n+2) = 48 → n² + 2n − 48 = 0.
Question 7: The graph of y = x² − 2x − 8 crosses the x-axis at two points. What is the distance between these x-intercepts?
- 4
- 5
- 6 (Correct answer)
- 8
Correct answer: 6
Factor: (x−4)(x+2) = 0 → x = 4 or x = −2; distance = |4 − (−2)| = 6.
Bluebook SAT Test Nonlinear Equations and Systems 3
Which of the following is equivalent to x² − 16?