F(x) is a polynomial whose degree is atleast 3. When it is divided by x-5, the remainder is 17. When F(x) is divided by x-6, the remainder is 19. Find the remainder when F(x) is divided by (x-5) (x-6).

Question

Answer 1

dividend = d*q+remainder
f(x)=(x-5)q1+17
f(5)=0+17
f(x)=(x-6)q2+19
f(6)=0+19
let ax+b be the remainder when divided by (x-5)(x-6)
f(x)=(x-5)(X-6)q3+ax+b
f(5)=0+5a+b
f(6)=0+6a+b
f(5)=17=5a+b
f(6)=19=6a+b
subtract
a=2
b=7
remainder=2x+7

Answer 2

dividend = d*q+remainder
f(x)=(x-5)q1+17
f(5)=0+17
f(x)=(x-6)q2+19
f(6)=0+19
let ax+b be the remainder when divided by (x-5)(x-6)
f(x)=(x-5)(X-6)q3+ax+b
f(5)=0+5a+b
f(6)=0+6a+b
f(5)=17=5a+b
f(6)=19=6a+b
subtract
a=2
b=7
remainder=2x+7

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F(x) is a polynomial whose degree is atleast 3. When it is divided by x-5, the remainder is 17. When F(x) is divided by x-6, the remainder is 19. Find the remainder when F(x) is divided by (x-5) (x-6).