Question

When a polynomial f(x) is divided by x-3 and x+6 , the respective remainders are 7 and 22. What is the remainder when f(x) is divided by (x-3)(x+6)​

Answer 1

Answer:

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p(x) is divided by (x-1) , the remainder is 3. Then

p(1)=3…………….(1)

p(x) is divided by (x-3) , the remainder is 5. Then

p(3)=5……………..(2)

p(x) is divided by (x-3).(x-1), the remainder is r(x) .Then

p(x)= q.(x-3).(x-1) +r(x). , putting r(x) = m.x+n

p(x)= q.(x-3).(x-1)+ m.x+n…………….(3)

Putting x=1 in eqn. (3)

p(1)=q.(-2).(0)+m.1+n

or. 3= m+n………………..(4)

Putting x=3 in eqn. (3)

p(3)=q.(0).(2)+m.3+n

or. 5= 3m+n………………(5). , by solving eqn. (4) & (5). m=1 , n= 2.

Thus , r(x)= x+2. , putting x=-2

r(-2) = -2+2.

r(-2) = 0.

Answer 2

Step-by-step explanation:

REFER TO THE ATTACHMENT ❤️