If (x+a) is a factor of two polynomials x^2+px+q and x^2+mx+n, then prove that : a=n- q/m-p.

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𝗜𝗳 𝘅+𝗮 𝗶𝘀 𝗮 𝗳𝗮𝗰𝘁𝗼𝗿 𝗼𝗳 𝘁𝗵𝗲 𝗽𝗼𝗹𝘆𝗻𝗼𝗺𝗶𝗮𝗹𝘀 𝘅𝟮+𝗽𝘅+𝗾 𝗮𝗻𝗱 𝘅𝟮+𝗺𝘅+𝗻.𝗧𝗵𝗲𝗻 𝗽𝗿𝗼𝘃𝗲 𝘁𝗵𝗮𝘁 𝗮= 𝗻-𝗾/𝗺-𝗽 𝗹𝗹 𝗣𝗼𝗹𝘆𝗻𝗼𝗺𝗶𝗮𝗹𝘀 𝗜𝗳 𝘅+𝗮 𝗶𝘀 𝗮 𝗳𝗮𝗰𝘁𝗼𝗿 𝗼𝗳 𝘁𝗵𝗲 𝗽𝗼𝗹𝘆𝗻𝗼𝗺𝗶𝗮𝗹𝘀 𝘅𝟮+𝗽𝘅+𝗾 𝗮𝗻𝗱 𝘅𝟮+𝗺𝘅+𝗻.𝗧𝗵𝗲𝗻 𝗽𝗿𝗼𝘃𝗲 𝘁𝗵𝗮𝘁 𝗮= 𝗻-𝗾/𝗺-𝗽 𝗹𝗹 𝗣𝗼𝗹𝘆𝗻𝗼𝗺𝗶𝗮𝗹𝘀
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