Question

Find the remainder when p(x)= x^3-6x^2+2x-4 and g(x)= 1-3/2 x

Answer 1

Answer:

Here, g(x)=3x−1. To apply Remainder theorem, (3x−1) should be converted to (x−a) form.

∴3x−1=

3

1

(3x−1)=x−

3

1

∴g(x)=(x−

3

1

)

By remainder theorem, r(x)=p(a)=p(

3

1

)

p(x)=x

3

−6x

2

+2x−4⇒p(

3

1

)=(

3

1

)

3

−6(

3

1

)

2

+2(

3

1

)−4

=

27

1

−

9

6

+

3

2

−4=

27

1−18+18−108

=

27

−107

∴ the remainder p(

3

1

)=−

27

107