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 :
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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
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