Question

Find the remainder when x⁵ is divided by (x-1)³ with there is no term of remainder in x² with the constant term is also zero​

Answer 1

Answer:

Correct option is

A

−90

(x–1)(x–2)(x–3)=x

3

–6x

2

+11x–6

Let the quotient and remainder when

x

5

+kx

2

is divided by (x–1)(x–2)(x–3) be

(ax

2

+bx+c) and dx+e

Now

x

5

+kx

2

=(x

3

–6x

2

+11x–6)(ax

2

+bx+c)+dx+e

Comparing the coefficients of x

5

,x

4

,x

3

andx

2

we get

a=1

b – 6 a = 0 ⇒ b = 6

c – 6 b + 11 a = 0 ⇒ c = 25

–6c+11b–6a=k

⇒ k = –90

Hence, the value of k is –90

Step-by-step explanation:

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