Question

Divide p(x) by g(x) and find the quotient and remainder where p(x) = x3-2x2 + 6x + 5 and g(x) = x+l.. asap

Answer 1

Answer:

The division of p(x)=x

3

+4x

2

−5x+6 by g(x)=x+1 is as shown above:

Now we know that the division algorithm states that:

Dividend=(Divisor×quotient)+Remainder

Here, the dividend is x

3

+4x

2

−5x+6, the divisor is x+1, the quotient is x

2

+3x−8 and the remainder is 14, therefore,

x

3

+4x

2

−5x+6=[(x+1)(x

2

+3x−8)]+14

⇒x

3

+4x

2

−5x+6=[x(x

2

+3x−8)+1(x

2

+3x−8)]+14

⇒x

3

+4x

2

−5x+6=x

3

+3x

2

−8x+x

2

+3x−8+14

⇒x

3

+4x

2

−5x+6=x

3

+3x

2

+x

2

−8x+3x−8+14

⇒x

3

+4x

2

−5x+6=x

3

+4x

2

−5x+6

Hence, the division algorithm is verified.