Question

f(x) = x⁴. 2x³ + 3x² - ax + b leave remainder 5 and 19 on division by (x-1) and x+1 respectively. find the remainder when f(x) is divided by x-2​

Answer 1

Answer:

34

Step-by-step explanation:

This question can be done through remainder theorem,

when divided by (x-1), remainder is 5

f(1)=1^4+2(1)^3+3(1)^2-a(1)+b=5

1+2+3-a+b=5

6-a+b=5

b-a= -1 ---------eq 1

when divided by (x+1), remainder is 19

f(-1)= (-1)^4+2(-1)^3+3(-1)^2-a(-1)+b=19

1-2+3+a+b=19

a+b=17 -------eq 2

Therefore solving 1 and 2 we get,

a=9 , b=8

Therefore when divided by (x-2)

f(x) = x⁴+2x³ + 3x² - ax + b

(2)^4+2(2)^3+3(2)^2-2(9)+8

= 16 +16 +12 - 18 +8

= 34 (Ans)