Question

please answer

for your help
answer = (a=5,b=8) remainder =10

full solution needed​

Answer 1

p(x)= x^4 -2x^3 + 3x^2- ax+ b

when divided by (x-1) it leaves remainder 5

So p( x) -5 becomes divisible by ( x-1)

x^4 - 2 x^3 + 3x^2 - ax + b -5 is divisible by ( x-1)

Put x= 1

then p( 1) -5 = 0

1- 2 + 3 - a+b = 5

- a+ b= 3 ........(1)

Also p( x) when divided by ( x+1) leave remainder 19

So p( x)-19 is divisible by ( x+1)

p( -1) -19 = 0

1+ 2+3+a+ b= 19

a+ b = 13

-a+ b= 3( from 1)

Add

2b = 16

b= 8

a+ b= 13

a= 13-b = 13-8 = 5

Remainder when p(x) is divided by x-2

let remainder be L

p( x) - L becomes divisible by x-2

p( 2) - L = 0

16 -16 +12- 2a + b = L

12 -2(5) +8= L

12 -10+8= L

10= L

Answer 2

so here is your answer

pls refer to both the attachment

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