Question

Q. Factorize:-
$x^4+x^2+25$

Answer 1

Dear Student,

$$\begin{gathered} x^4+x^2+25 \\ Addingandsubtracting10x^2,weget \\ {x}^4+x^2+25+10x^2-10x^2 \\ {x}^4+10x^2+25-10x^2+x^2 \\ {x}^4+10x^2+25-9x^2 \\ \left[\mathbf{U}\mathbf{s}\mathbf{i}\mathbf{n}\mathbf{g}\mathbf{}{\left(\mathbf{a}\mathbf{+}\mathbf{b}\right)}^{\mathbf{2}}\mathbf{}\mathbf{=}\mathbf{}{\mathbf{a}}^{\mathbf{2}}\mathbf{+}{\mathbf{b}}^{\mathbf{2}}\mathbf{+}\mathbf{2}\mathbf{a}\mathbf{b}\right] \\ {\left(x^2+5\right)}^2-9x^2 \\ \left[\mathbf{U}\mathbf{s}\mathbf{i}\mathbf{n}\mathbf{g}\mathbf{}{\mathbf{a}}^{\mathbf{2}}\mathbf{-}{\mathbf{b}}^{\mathbf{2}}\mathbf{=}\left(\mathbf{a}\mathbf{-}\mathbf{b}\right)\left(\mathbf{a}\mathbf{+}\mathbf{b}\right)\right] \\ \left[\left(x^2+5\right)-3x\right]\left[\left(x^2+5\right)+3x\right] \\ \left({\mathbf{x}}^{\mathbf{2}}\mathbf{+}\mathbf{5}\mathbf{-}\mathbf{3}\mathbf{x}\right)\left({\mathbf{x}}^{\mathbf{2}}\mathbf{+}\mathbf{5}\mathbf{+}\mathbf{3}\mathbf{x}\right) \end{gathered}$$

Regards