Let’s resolve into factors

p² + 31pq + 108q²

To resolve it into factors we first resolve 108

108=2×2×3×3×3

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

Comparing 1 and 2

m + n =31

mn =108

∴ (1) can be written as

p² + 27pq + 4pq + 108q²

= (p + 27q)( p + 4q)

∴ The resolved factors are (p + 27q)( p + 4q)