Q. 484.8( 4 Votes )

Factorize:

4x4 + 7x2 – 2

Answer :

We have,



Now by using middle-term splitting, we get


= 4y2 + 7y – 2


= 4y2 + 8y – y – 2


= 4y (y + 2) – (y + 2)


= (y + 2) (4y – 1)


Now,


Replacing y by x2, we get


4x4 + 7x2 – 2


= (x2 + 2) (4x2 – 1) [Therefore, a2 – b2 = (a – b) (a + b)]


= (x2 + 2) (2x + 1) (2x – 1)


Hence,


The given expression can be factorized as:



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