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How many polynomials exist which interpolate the data where for?

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How many polynomials exist which interpolate the data<br><img src='https://www.fatskills.com/images2/GradExams/77F7B44F-4631-4B0B-889A-DB42716F77DD.png' height='20' width='238'/> where<br><img src='https://www.fatskills.com/images2/GradExams/F5C9D3B1-0B38-44A2-BFDD-0BD16D44FCA2.png' height='21' width='60'/> for<br><img src='https://www.fatskills.com/images2/GradExams/60E21A71-8621-47C9-AF92-63773FDF86DD.png' height='20' width='41'/>?






 
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