Factorize: X4 + X2 + 25. - Mathematics

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Answer in Brief

Factorize: x4 + x2 + 25.

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Solution

The given expression to be factorized is  x4 + x2 + 25

This can be written in the form

x4 + x2 + 25= ` (x^2)^2 + 2x^2 .5 + (5)^2 - 9x^2`

                  ` = {(x^2)^2 + 2x^2 .5 + (5)^2}- (3x)^2`

                  ` = (x^2 + 5)^2 - (3x)^2`

` = (x^2 + 5 + 3x) (x^2 + 5 - 3x)`

We cannot further factorize the expression. 

So, the required factorization is. `x^4  + x^2 + 25 = (x^2 + 5+3x)(x^2 + 5 - 3x)`

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Chapter 5: Factorisation of Algebraic Expressions - Exercise 5.5 [Page 25]

APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 5 Factorisation of Algebraic Expressions
Exercise 5.5 | Q 9 | Page 25

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