Question

If f(x)=x^4-2x^3+3x^2-ax+b a polynomial is divided by x-1 and x+1 remainders are 5 and 9 respectively. determine the remainder when f(x) is divided by x-2

Answer 1

Answer:

first the thing to do is:

x-1=0

x=1

substitute x as 1 in the equation and put equal to 5 as remainder.

like this:

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

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

f(1)=2-a+b=5

f(1)= -a+b=5-2

-a+b=3

Now,do the same for x+1

x+1=0

x= -1

use it in the equation f(x) and equal to 9 respectively.

like this:

f(-1)=(-1)^4-2(-1)^3+3(-1)^2-a(-1)+b=9

f(-1)=(1)-2(-1)+3(1)+a+b=9

f(-1)=1+2+3+a+b=9

f(-1)=6+a+b=9

f(-1)=a+b=9-6

a+b=3

now,f(x)=F(x)

-a+b-3=a+b-3

-2a=0

a=2

now,substitute a =2 in f(x) and u will find b.AND with that u can find remainder when divided by x-2.

hope it helps

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