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निम्न व्यंजकों के गुणनखण्ड इनके मध्य पद को विभक्त करके कीजिए(i) x4 + 3x2 – 28(ii) x4 – 5x2 + 4 |
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Answer» (i) x4 + 3x2 – 28 = x4 + (7 – 4)x2 – 28 (∵ 28 = 2 × 2 × 7) = x4 + 7x2 – 4x2 – 28 = x2(x2 + 7) – 4(x2 + 7) = (x2 + 7)(x2 – 4) = (x2 + 7)[(x)4 – (2)4] = (x2 + 7)(x + 2)(x – 2) (ii) x4 – 5x2 + 4 = x4 – (1 + 4)x2 + 4 (∵ 4 = 1 × 4) = x4 – x2 – 4x2 + 4 = x2(x2 – 1) – 4(x2 – 1) = (x2 – 1)(x2 – 4) = [(x)2 – (1)2][(x2) – (2)2] = (x + 1)(x – 1)(x + 2)(x – 2) |
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