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Equivalent Expressions

SAT Math· difficulty 5/5

Which is equivalent to x4−5x2+4x^4 - 5x^2 + 4?

  • A

    (x2−4)2(x^2 - 4)^2

  • B

    (x−2)2(x+2)2(x - 2)^2(x + 2)^2

  • C

    (x−1)(x+1)(x−2)(x+2)(x - 1)(x + 1)(x - 2)(x + 2)

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  • D

    (x2−1)(x2+4)(x^2 - 1)(x^2 + 4)

Explanation

Treat as quadratic in x2x^2: u2−5u+4=(u−1)(u−4)=(x2−1)(x2−4)=(x−1)(x+1)(x−2)(x+2)u^2 - 5u + 4 = (u - 1)(u - 4) = (x^2 - 1)(x^2 - 4) = (x-1)(x+1)(x-2)(x+2).

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