Question

Factorise the following x^4+x

Answer 1

Answer:

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

Step-by-step explanation:

$x^4=x\cdot \underbrace{x\cdot x\cdot x}_{3}=x\cdot x^3\\\\x=x\cdot 1\\\\x^4+x=\bold{x}\cdot x^3+\bold{x}\cdot1=\bold{x}\cdot(x^3+1)\\\\\text{used the distriburtive property:}\ a(b+c)=ab+ac$

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

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

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