Bluebook SAT Test Equivalent Expressions 7

Question 1

Which of the following is equivalent to 2x² + 5x − 3?

Accepted Answer

(2x − 1)(x + 3)

Answer

(2x − 1)(x + 3) = 2x² + 6x − x − 3 = 2x² + 5x − 3 ✓.

Question 2

Which of the following is equivalent to ((x²y)/(z))²?

Accepted Answer

x⁴y²/z²

Answer

Apply the power to each part: (x²)² = x⁴, y² = y², z² = z²; result = x⁴y²/z².

Question 3

Which of the following is equivalent to (2x − 1)/(3) + (x + 2)/(3)?

Accepted Answer

(3x + 1)/3

Answer

Add numerators over common denominator: (2x − 1 + x + 2)/3 = (3x + 1)/3.

Question 4

Which of the following is equivalent to (x² − 2x − 8)?

Accepted Answer

(x − 4)(x + 2)

Answer

Find two numbers that multiply to −8 and add to −2: −4 and +2; so (x − 4)(x + 2).

Question 5

Which of the following is equivalent to a⁰ for any nonzero value of a?

Accepted Answer

1

Answer

Any nonzero number raised to the power 0 equals 1, by definition of the zero exponent rule.

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