Question

Factorise :
x⁴ + x² + 1
​

Answer 1

Answer:

(x²+1+x) (x²+1-x)

Step-by-step explanation:

....hope this helps u !!

Answer 2

Topic :-

Factorisation

To Factorise :-

$x^4+x^2+1$

Method :-

We generally try to solve such questions by making it in form of a² - b² and then further factorising it as ( a + b )( a - b ).

Solution :-

$x^4+x^2+1$

Add and Subtract x²,

$x^4+x^2+x^2-x^2+1$

Rearrange it,

$x^4+2x^2+1-x^2$

We can observe,

a² + 2ab + b² = ( a + b )² forming here,

Grouping some terms,

$(x^2)^2+2(x^2)(1)+(1^2)-x^2$

$(x^2+1)^2-x^2$

Now, we can observe,

a² - b² = ( a + b )( a - b ) formula here,

Using formula,

$(x^2+1+x)(x^2+1-x)$

It is factorised!!

Additional Factorization to Remember :-

a³ + b³ = ( a + b )( a² - ab + b² )

a³ - b³ = ( a - b )( a² + ab + b² )

x⁴ - y² + 2x² + 1 = ( x² + 1 + y )( x² + 1 - y )

a⁴ - b⁴ = ( a² + b² )( a + b )( a - b )