Factorise completely x^4-12x^2+13

Answer 1

To factorise the expression x^4 - 12x^2 + 13 completely, we can treat it as a quadratic equation in x^2.

Let's denote y = x^2. Then the given expression can be rewritten as y^2 - 12y + 13.

Now, we need to factorise the quadratic equation y^2 - 12y + 13. This can be factored as (y - 1)(y - 13).

Substitute back y = x^2, we get the factors, (x^2 - 1)(x^2 - 13).

Further factorising each quadratic factor, we get:

(x + 1)(x - 1)(x^2 - 13)

Therefore, the expression x^4 - 12x^2 + 13 is completely factorised as (x + 1)(x - 1)(x^2 - 13).