Question

If (5x² + 14x + 2)² is divided by x² + x + 1, then the quotient q and the remainder r are given by :

(a) q = (x² + 19x - 5), r = 1

(b) q = 9(x² + 19x - 5), r = 0

(c) q = (x² + 19x - 5), r = 0

(d) q = 9(x² + 19x - 5), r = 1

Answer 1

Correct option is (c) q = (x² + 19x - 5), r = 0

As given (5x² + 14x + 2)² − (4x² − 5x + 7)² is divided by x² + x + 1

= ((5x² + 14x − 5) − (4x² − 5x + 7))((5x² + 14x + 2) + (4x² − 5x + 7))

= (5x² + 14x + 2 − 4x² + 5x − 7)(5x² + 14x + 2 + 4x² − 5x + 7)

= (x² + 19x − 5)(9x² + 9x + 9)

= (x² + 19x − 5)9(x² + x + 1)

Now dividing by x² + x + 1

\(= \frac{(x^2 + 19x -5)9(x^2 + x + 1)}{x^2 + x + 1}\)

Quotient = 9(x² + 19x − 5) and Reminder = 0