Answer:
[tex]\large\boxed{x^4+x=x(x^3+1)=x(x+1)(x^2-x+1)}[/tex]
Step-by-step explanation:
[tex]x^4=x\cdot \underbrace{x\cdot x\cdot x}_{3}=x\cdot x^3\\\\x=x\cdot 1\\\\x^4+x=\bold{x}\cdot x^3+\bold{x}\cdot1=\bold{x}\cdot(x^3+1)\\\\\text{used the distriburtive property:}\ a(b+c)=ab+ac[/tex]
[tex]\text{If you want complete factorise, then:}[/tex]
[tex]x^3+1=x^3+1^3[/tex] [tex]\text{use}\ a^3+b^3 = (a + b)(a^2 - ab + b^2)[/tex]
[tex]x^4+x=x(x^3+1)=x(x+1)(x^2+(x)(1)+1^2)=x(x+1)(x^2+x+1)[/tex]
