Let’s resolve into factors

x⁴-7x² + 12

(x²)²-7x² + 12 … (1)

To resolve it into factors we first resolve 12

12=1×2×2×3

Given, x² + (m + n)x + mn=(x + m)(x + n) … (2)

Comparing 1 and 2

m + n =-7

mn =12

∴ (1) can be written as

(x²)²-3x²-4x² + 12

= x²(x² – 3) – 4(x² – 3)

= (x²-4)( x²-3)
We know a² – b² = (a – b)(a+b)

= (x-2)(x+2)( x²-3)

∴ The resolved factors are (x-2)(x+2)( x²-3)