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Q.

For a polynomial, the divisor g(x) = 3x − 2, quotient q(x) = 6x2 + 4, and the remainder r(x)= 5. Find the dividend p(x). 

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a

18x3 − 12x2 + 12x − 3

b

12x3 − 12x2 + 12x − 3 

c

12x3 − 18x2 + 3x − 12 

d

x3 − 12x2 + 12x − 3 

answer is A.

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Detailed Solution

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We know that, p(x )= q(x) × g(x) + r(x) 

Substituting the values, we get:

p(x) = (6x2 + 4) × (3x − 2) + 5  

On multiplying q(x) and g(x), we get:  

p(x) =  (18x3 + 12x − 12x2 − 8) + 5  

p(x) = 18x3 + 12x − 12x2 − 8 + 5 

p(x) = 18x3 + 12x − 12x2 − 3

Therefore, the dividend, p(x) = 18x3 + 12x − 12x2 − 3.

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