Question

find the remainder and quotient when x power 3 + 4x power 2 + 3x – 6 polynomial is divided by x + 2

Answer 1

Hi ,

let p( x ) = x³ + 4x² + 3x - 6

By remainder theorem ,

if p( x ) is divided by x + 2 then the remainder

is p( -2 )

p( -2 ) = ( -2 )³ + 4 ( -2 )² + 3 ( -2 ) - 6

= -8 + 16 - 6 - 6

= -20 + 16

= - 4

Therefore ,

Required remainder = -4

I hope this helps you.

:)

2nd method :
__________

long division method :

x+2)x³+4x²+3x-6(x²+2x-1
-----x³+2x²
_____________
---------2x²+3x
---------2x²+4x
____________
-x -6
-x - 2
______________
-4

remainder = -4

quotient = x² + 2x - 1

I hope this helps you.

:)