Question

factorize x^4+x^2+1
step by step​

Answer 1

Answer:

There are multiple ways for factorizing

Step-by-step explanation:

Approach # 1:

x4+x2+1=x4+x3+x2−x3−x2−x+x2+x+1x4+x2+1=x4+x3+x2−x3−x2−x+x2+x+1

=>x2(x2+x+1)−x(x2+x+1)+(x2+x+1)=>x2(x2+x+1)−x(x2+x+1)+(x2+x+1)

=>(x2+x+1)∗(x2−x+1)=>(x2+x+1)∗(x2−x+1)

Approach # 2:

Let y=x2y=x2

=>x4+x2+1=y2+y+1=>x4+x2+1=y2+y+1

Let us find the roots

y2+y+1=0y2+y+1=0

=>y=−1±1–4√2=>y=−1±1–42

=>y=12∗(−1±3–√i)=>y=12∗(−1±3i)

=>y=x2=