Question

Find the remainder when x^4 + 4x^3 – 5x^2 – 6x +7 when divided by ) 2x -1

Answer 1

Answer:

-47

Step-by-step explanation:

We divide x

4

+4x

3

−5x

2

−6x+7 by (x+3) as shown in the above image:

From the division, we observe that the quotient is x

3

+x

2

−8x+18 and the remainder is −47.

Hence, the remainder is

Answer 2

Answer:

Answer:

Here one root is x = 1 so (x - 1) is a factor. i.e

{x}^{3} - {x}^{2} - 3 {x}^{2} + 3x + 2x - 2 =x

3

−x

2

−3x

2

+3x+2x−2=

{x}^{2} (x - 1) - 3x(x - 1) + 2(x - 1) =x

2

(x−1)−3x(x−1)+2(x−1)=

(x - 1)( {x}^{2} - 3x + 2) =(x−1)(x

2

−3x+2)=

(x - 1)( {x}^{2} - 2x - x + 2) =(x−1)(x

2

−2x−x+2)=

(x - 1)(x(x - 2) - 1(x - 2)) =(x−1)(x(x−2)−1(x−2))=

(x - 1)(x - 2)(x - 1) = (x - 1) {}^{2} (x - 2)(x−1)(x−2)(x−1)=(x−1)

2

(x−2)