Factorize each of the following algebraic expression:

Question:

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

Solution:

$a^{4}+3 a^{2}+4$

$=\mathrm{a}^{4}+4 \mathrm{a}^{2}-\mathrm{a}^{2}+4$

$=\left(\mathrm{a}^{4}+4 \mathrm{a}^{2}+4\right)-\mathrm{a}^{2}$

$=\left[\left(\mathrm{a}^{2}\right)^{2}+2 \times \mathrm{a}^{2} \times 2+2^{2}\right]-\mathrm{a}^{2}$

$=\left(\mathrm{a}^{2}+2\right)^{2}-\mathrm{a}^{2}$

$=\left[\left(\mathrm{a}^{2}+2\right)-\mathrm{a}\right]\left[\left(\mathrm{a}^{2}+2\right)+\mathrm{a}\right]$

$=\left(\mathrm{a}^{2}-\mathrm{a}+2\right)\left(\left(\mathrm{a}^{2}+\mathrm{a}+2\right)\right.$

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