Question

factorize =( x⁴ + 4x² + 3)​

Answer 1

Answer:

Given information:

The given expression is $x^{4}+4x^2+3$.

To factorize the given expression.

Apply the process of spliting the middle term.

Step-by-step explanation:

Splitting of Middle Term which is $x^2$ term is the sum of two factors and product equal to last term.

The sum of two factors $x^2$ and $3x^2$ is $4x^2$.

The product of two factors $x^2$ and $3x^2$ is $3x^4$.

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

The factorize form of the given expression is $(x^2+1)(x^2+3)$.