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1.How to use Remainder Theorem if the divisor in not linear (i.e:- it is quadratic or cubic)2.How to use remainder theorem if the divisor is x^3-1 (Please solve with steps and detailed explanation)Don’t write unnecessary answers pleaseI am not able to find this answer and stuck in maths Please Answer

Answer»

Step-by-step explanation:

1. as you know

Dividend=Divisor×Quotient+REMAINDER

  • when divisor is quadratic, then the remainder will be linear

for eg.

p(x) =

{x}^{17} + 2x ^{10} + 3 {x}^{5} + 2x - 1

and divisor = x^2-1 & THEREFORE remainder=ax+b

p(x)=(x+1)(x-1)Q(x)+ax+b

on putting x=1

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

a+b =7.........1

on putting x=-1

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

-a+b= -5.......2

on solving equation 1&2 we get

b=1 & a=6

Remainder=ax+b=6x+1

  • 2 In the case when divisor is cubic like px^3+qx^2+rx+s then remainder BECOMES quadratic ax^2+bx+c



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