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Question
Factorize `x^2 + 5sqrt5x + 30`
Solution
Splitting the middle term,
`= x^2 + 2sqrt5x + 3sqrt5x + 30` `[∵ 5sqrt5 = 2sqrt5 + 3sqrt5 " also " 2sqrt5 xx sqrt3 = 30]`
`= x(x + 2sqrt5) + 3sqrt5(x + 2sqrt5)`
`= (x + 2sqrt5)(x + 3sqrt5)`
`∴ x^2 + 5sqrt5x + 30 = (x + 2sqrt5)(x + 3sqrt5)`
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