Question

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 please
I am not able to find this answer and stuck in maths
Please Answer

Answer 1

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