Question

The polynomial f(x) = 4 - 2 3 + 3 2 – a x + b when divided by (x – 1) and (x + 1) leaves the remainders 5 and 19 respectively. Find the value of a and b . Hence, find the remainder when f(x) is divided by (x – 3)​

Answer 1

Answer:

47 see solution

Step-by-step explanation:

A polynomial f(x) is divided by a linear polynomial (x-a) leaves remainder which equal f(a).

so, f(x)=x

4

−2x

3

+3x

2

−ax+b

so, when it is divided by (x-1) it will leave a remainder

f(1)=5

⇒a−b=−3⟶(1)

similarly,

f(−1)=19

⇒a+b=13⟶(2)

solving(1)and(2)weget

a=5andb=8

∴thepolynomialis

f(x)=x

4

−2x

3

+3x

2

−5x+8

alsowhenitisdividedby(x−3)leavesremainder

f(3)=47