Bluebook SAT Test Equivalent Expressions 6

Question 1

Which of the following is equivalent to 9x² − 30x + 25?

Accepted Answer

(3x − 5)²

Answer

9x² − 30x + 25 = (3x)² − 2(3x)(5) + 5² = (3x − 5)².

Question 2

Which expression is equivalent to (x² − 5x + 4)/(x − 1)?

Accepted Answer

x − 4

Answer

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)?

Accepted Answer

x^−2

Answer

x³ · x⁻⁵ = x^(3 + (−5)) = x^(−2).

Question 4

Which of the following is equivalent to (3x)/(x − 2) + (6)/(x − 2)?

Accepted Answer

3(x + 2)/(x − 2)

Answer

(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?

Accepted Answer

−2x(x − 6)

Answer

Expand: −2(x² − 6x + 9) + 18 = −2x² + 12x − 18 + 18 = −2x² + 12x = −2x(x − 6).

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