Bluebook SAT Test Equivalent Expressions 4

Question 1

Which of the following is equivalent to (2x + 1)(x² − 3x + 2)?

Accepted Answer

2x³ − 5x² + x + 2

Answer

Expand: 2x(x² − 3x + 2) + 1(x² − 3x + 2) = 2x³ − 6x² + 4x + x² − 3x + 2 = 2x³ − 5x² + x + 2.

Question 2

If 3x² − 27 = 0, which factored form represents the left side?

Accepted Answer

3(x − 3)(x + 3)

Answer

3x² − 27 = 3(x² − 9) = 3(x − 3)(x + 3) by difference of squares.

Question 3

Which of the following is equivalent to x⁻³?

Accepted Answer

1/x³

Answer

A negative exponent means taking the reciprocal: x⁻³ = 1/x³.

Question 4

Which of the following is equivalent to (3x − 2)/5 + (x + 1)/5?

Accepted Answer

(4x − 1)/5

Answer

Same denominator: (3x − 2 + x + 1)/5 = (4x − 1)/5.

Question 5

Which expression is equivalent to (x − 4)² − (x + 4)²?

Accepted Answer

−16x

Answer

(x − 4)² − (x + 4)² = (x² − 8x + 16) − (x² + 8x + 16) = −16x.

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