Question

Factorize each of the following algebraic expression:
a⁴ + 3a² +4

Answer 1

$$\begin{gathered} {\mathrm{a}}^4+3{\mathrm{a}}^2+4 \\ ={\mathrm{a}}^4+4{\mathrm{a}}^2-{\mathrm{a}}^2+4 \\ =({\mathrm{a}}^4+4{\mathrm{a}}^2+4)-{\mathrm{a}}^2 \\ =\left[\right({\mathrm{a}}^2{)}^2+2\times {\mathrm{a}}^2\times 2+2^2]-{\mathrm{a}}^2 \\ =({\mathrm{a}}^2+2{)}^2-{\mathrm{a}}^2 \\ =\left[\right({\mathrm{a}}^2+2)-\mathrm{a}]\left[\right({\mathrm{a}}^2+2)+\mathrm{a}] \\ =({\mathrm{a}}^2-\mathrm{a}+2)\left(\right({\mathrm{a}}^2+\mathrm{a}+2) \end{gathered}$$