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Question

x2-qx-p2+5pq-6q2

ans (x-p-2q)(x+p-3q)

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Solution

= x^2 - qx - (p^2 - 5pq + 6q^2)
= x^2 - qx - (p-2q) (p-3q)
= x^2 - [(p-2q) - (p-3q)] x - (p-2q) (p-3q)
= x^2 - (p-2q) x + (p-3q) x - (p-2q) (p-3q)
= x (x - (p-2q)) + (p-3q) (x - (p-2q))
= (x - (p-2q)) (x + (p-3q))
= (x - p + 2q) (x + p - 3q)

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