Ex 2.3, 3 - Check whether 7 + 3x is a factor of 3x3 + 7x - Check if factor

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Ex 2.3, 3 Check whether 7 + 3x is a factor of 3x3 + 7x. Finding remainder when 3x3 + 7x is divided by 7 + 3x Step 1: Put Divisor = 0 7 + 3x = 0 3x = –7 x = (−7)/3 Step 2: Let p(x) = 3x3 + 7x Putting x = (−7)/3 p((−7)/3) = 3((−7)/3)^3 + 7((−7)/3) = − 3 (7^3/3^3 ) – 49/3 = − 243/9 – 49/3 = (−243 − 49(3))/9 = (−243 −147)/9 = (−490)/9 Thus, remainder = p((−7)/3) = (−490)/9 Since, remainder is not 0 Thus, 7 + 3x is a not factor of 3x3 + 7x

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