Bluebook SAT Test Equivalent Expressions 5

Question 1

Which of the following is equivalent to (x² − 4x − 21)/(x − 7)?

Accepted Answer

x + 3

Answer

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?

Accepted Answer

4xy²(3xy − 2)

Answer

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?

Accepted Answer

4xy

Answer

(x² + 2xy + y²) − (x² − 2xy + y²) = 4xy.

Question 4

Which of the following is equivalent to (x² + 4)/(x + 2)?

Accepted Answer

x − 2 + 8/(x + 2)

Answer

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)?

Accepted Answer

(3x + 4)(x − 2)

Answer

Factor out (x − 2): 3x(x − 2) + 4(x − 2) = (3x + 4)(x − 2).

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