Question

Find the remainder, when x4 + 4x3 - 5x2 - 6x + 7 is divided by x+1

Answer 1

Solution:-

• we have two methods to solve this type of question

Method:-1

Given polynomial is x⁴ + 4x³ - 5x² - 6x + 7 , it is divided by x + 1

Take ,x+ 1

x + 1 = 0

x = - 1

Now put the value of x on given polynomial:-

x⁴ + 4x³ - 5x² - 6x + 7 we get

( - 1 )⁴ + 4 × ( - 1 )³ - 5 × ( - 1 )² - 6 × ( - 1 ) + 7

1 - 4 - 5 + 6 + 7

5

So remainder is 5

Method:-2

Note method 2 solution given in attachment

Answer 2

Step-by-step explanation:

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)