Question

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Factorise x4+4x²-12

Answer 1

$x^4 + 4x^2 - 12 \\ \\ = (x^2)^2 + (2 \times x^2 \times 2) + 2^2 - 2^2 - 12 \\ \\ = (x^2 + 2)^2 - 4 - 12 \\ \\ = (x^2 + 2)^2 - (4 + 12) \\ \\ = (x^2 + 2)^2 - 16 \\ \\ = (x^2 + 2)^2 - 4^2 \\ \\ = (x^2 + 2 + 4)(x^2 + 2 - 4) \\ \\ = (x^2 + 6)(x^2 - 2)$

$\therefore x^4 + 4x^2 - 12 = (x^2 + 6)(x^2 - 2)$

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