Question

Factorise the following x^4+x

Answer 1

`\large\boxed{x^4+x=x(x^3+1)=x(x+1)(x^2-x+1)}`

Explanation:

`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`

`\text{If you want complete factorise, then:}`

`x^3+1=x^3+1^3`
`\text{use}\ a^3+b^3 = (a + b)(a^2 - ab + b^2)`

`x^4+x=x(x^3+1)=x(x+1)(x^2+(x)(1)+1^2)=x(x+1)(x^2+x+1)`