Question # 01: Factorize each of the following expressions:
\((iv)\) \(\; \)\(x^4-14x^2+1 \)
Solution:
\(\ \ \ \ x^4-14x^2+1 \)
\(=x^{4} -14x^{2} +1+2x^{2} -2x^{2}\)
\(=x^{4} +2x^{2} +1-16x^{2}\)
\(=\left( x^{2}\right)^{2} -2\left( x^{2}\right)( 1) +( 1)^{2} -( 4x)^{2}\)
\(=\left( x^{2} +1\right)^{2} -( 4x)^{2}\)
\(=\left( x^{2} +1+4x\right)\left( x^{2} +1-4x\right)\)