Question

explain vanishing method and please also give examples

Answer 1

Use the factor theorem: r is a root of polynomial p if and only if x−r is a factor of p. Since 7 is a solution of x3−67x+126=0, 7 is a root of x3−67x+126 so x−7 divides x3−67x+126. You may use polynomial long division to factor out x−7, leaving a quadratic polynomial that you can factor in standard ways.

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