Question

the remainder when ax³ - bx²- x + 5 and x³ + ax² + 2x - b - 4 are divided by x + 1 are "-3" and 10 respectively, find a and b.​

Answer 1

Step-by-step explanation:

1. let first equation be p(x)=ax^3-bx^2-x+5
2. and second equation be q(x)=x^3+ax^2+2x-b-4
3. we have to find a and b

let b=0

when divided by x+1

=x+1=0

=x=0-1= -1

now put -1 at all place of x in both equations

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

-1a-b+1+5 = -1+a-2-b-4

-a-b-a+b=-1-5-1-2-4

(-a)-b =-12

-a=-12+b=0

-a=-12

12=a