Question

Factorise the following:

x⁴ – 5x² + 4

Answer 1

Given: x⁴ – 5x² + 4

Step-wise calculation:

1. Notice that the expression is a quadratic in terms of x². 

Let y = x², then the expression becomes y² – 5y + 4.

2. Factorize: y² – 5y + 4 = (y – 4)(y – 1).

Since –4 × –1 = 4 and –4 + –1 = –5.

3. Substitute back y = x²: (x² – 4)(x² – 1).

4. Each factor can be further factorized using the difference of squares formula:

x² – 4 = (x – 2)(x + 2)

x² – 1 = (x – 1)(x + 1)