Question

If (5x² +14x + 2)^2 – (4x2 – 5x+7)^2 is divided by x^2 +x+1, then the quotient q and the remainder r are given by :​

Answer 1

As given (5x

2

+14x+2)

2

−(4x

2

−5x+7)

2

is divided by x

2

+x+1

=((5x

2

+14x−5)−(4x

2

−5x+7))((5x

2

+14x+2)+(4x

2

−5x+7))

=(5x

2

+14x+2−4x

2

+5x−7)(5x

2

+14x+2+4x

2

−5x+7)

=(x

2

+19x−5)(9x

2

+9x+9)

=(x

2

+19x−5)9(x

2

+x+1)

Now dividing by x

2

+x+1

=

x

2

+x+1

(x

2

+19x−5)9(x

2

+x+1)

Quotient=9(x

2

+19x−5)andReminder=0