Question

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

Answer 1

\[a^4 + 3 a^2 + 4\]
\[ = a^4 + 4 a^2 - a^2 + 4\]
\[ = ( a^4 + 4 a^2 + 4) - a^2 \]
\[ = [( a^2 )^2 + 2 \times a^2 \times 2 + 2^2 ] - a^2 \]
\[ = ( a^2 + 2 )^2 - a^2 \]
\[ = [( a^2 + 2) - a][( a^2 + 2) + a]\]
\[ = ( a^2 - a + 2)(( a^2 + a + 2)\]