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Equivalent Expressions

SAT Math· difficulty 4/5

The expression x3+1x+1\dfrac{x^3 + 1}{x + 1} is equivalent to which expression for x≠−1x \ne -1?

  • A

    x2−1x^2 - 1

  • B

    x2+x+1x^2 + x + 1

  • C

    x2−x+1x^2 - x + 1

    check_circle
  • D

    x2+1x^2 + 1

Explanation

Sum of cubes: x3+1=(x+1)(x2−x+1)x^3 + 1 = (x+1)(x^2 - x + 1). Cancel (x+1)(x+1): x2−x+1x^2 - x + 1.

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