Question

Dividend p(x) = x^4 + 1 = x + 1 x+1 Diviser g(x) divide p [x) by g (x)​

Answer 1

Answer:

The division of p(x)=x

4

−3x

2

−4 by g(x)=x+2 is as shown above:

Now we know that the division algorithm states that:

Dividend=(Divisor×quotient)+Remainder

Here, the dividend is x

4

−3x

2

−4, the divisor is x+2, the quotient is x

3

−2x

2

+x−2 and the remainder is 0, therefore,

x

4

−3x

2

−4=[(x+2)(x

3

−2x

2

+x−2)]+0

⇒x

4

−3x

2

−4=[x(x

3

−2x

2

+x−2)+2(x

3

−2x

2

+x−2)]+0

⇒x

4

−3x

2

−4=x

4

−2x

3

+x

2

−2x+2x

3

−4x

2

+2x−4+0

⇒x

4

−3x

2

−4=x

4

−2x

3

+2x

3

+x

2

−4x

2

−2x+2x−4

⇒x

4

−3x

2

−4=x

4

−3x

2

−4

Hence, the division algorithm is verified.

Answer 2

Answer:

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