Question

Factorise-
x^4+5x^2+9

Answer 1

X4 + 5X2 + 9 

 X4 + 5X2  + X2 + 9     -  X2 

 X4 + 6X2  + 9      -  X2   group 3 and factor

 (X2  + 3) (X2  + 3)    -  X2 

 (X2  + 3) 2  -  X2   this is a difference of  squares

 (X2  + 3 – X) (X2  + 3 + X) rearrange

 (X2  – X +3) (X2  + X +3)

Answer 2

$(x^{2} - x + 3) (x^{2} + x + 3)$ are the factors of x^4 + 5x^2 + 9.

Step-by-step explanation:

To factorize:

$x^{4} + 5x^{2} + 9$

= $x^{4} + 6x^{2} + 9 - x^{2}$

= $(x^{2} + 3)^{2} - x^{2}$

= $(x^{2} - x + 3) (x^{2} + x + 3)$       ......by putting $x^{2} - y^{2}$ = (x + y)(x - y)

Thus, the factors of $x^4+5x^2+9$ are $(x^{2} - x + 3) (x^{2} + x + 3)$

Learn more: factorize

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