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Question
Factorise the following:
`sqrt(5)"a"^2 + 2"a" - 3sqrt(5)`
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Solution
Product = `sqrt(5) xx - 3sqrt(5)`, = −15, sum = 2
Split the middle term as 5x and −3x
`sqrt(5)"a"^2 + 2"a" - 3sqrt(5) = sqrt(5)"a"^2 + 5"a" - 3"a" - 3sqrt(5)`
= `sqrt(5)"a"("a" + sqrt(5)) - 3("a" + sqrt(5))`
= `("a" + sqrt(5))(sqrt(5)"a" - 3)`
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