The products of linear factors can be found using the formulas a2-b2=(a+b)(a-b)a2−b2=(a+b)(a−b) and a2+b2=(a-bi)(a+bi)a2+b2=(a−bi)(a+bi).
To write out x3+xx3+x as a product of linear factors, first factor out an xx and then use the formula a2+b2=(a-bi)(a+bi)a2+b2=(a−bi)(a+bi) on x2+1x2+1 where a=√x2=xa=√x2=x and b=√1=1b=√1=1.
x3+xx3+x
Factor out an xx.
==
x(x2+1)
Substitute into the formula a2+b2=(a-bi)(a+bi) where a=√x2=x and b=√1=1.
