Q5 of 65 Page 137

Let us factorise the following algebraic expressions:

x4 – 7x2 + 1

Given, x4 – 7x2 + 1


Can be written as


⇒ (x2 + 1)2 – 9x2


⇒ (x2 + 1)2 – (3x)2


[Since, from the identity III we know that, (x2 – y2) = (x – y)(x + y)]


⇒ ((x2 + 1) – 3x)((x2 + 1) + 3x)


⇒ (x2 – 3x + 1)(x2 + 3x + 1)


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