Question

Divide p(x) = 3x* + 5x® - 9x - 6x +12 by - x - 2x + 1 and hence verify the division algorithm. ​

Answer 1

The division of p(x)=2x

2

−9x+9 by g(x)=x−3 is as shown above:

Now we know that the division algorithm states that:

Dividend=(Divisor×quotient)+Remainder

Here, the dividend is 2x

2

−9x+9, the divisor is x−3, the quotient is 2x−3 and the remainder is 0, therefore,

2x

2

−9x+9=[(x−3)(2x−3)]+0

⇒2x

2

−9x+9=[x(2x−3)−3(2x−3)]

⇒2x

2

−9x+9=x

2

−3x−6x+9

⇒2x

2

−9x+9=2x

2

−9x+9

Hence, the division algorithm is verified.

Answer 2

Answer:

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