find the remainder when x cube minus 3 X square + 3 x minus 1 is divided by X + 3​

GIVEN

[tex]p(x) = {x}^{3} - 3 {x}^{2} + 3x - 1[/tex]

[tex]g(x) = x + 3[/tex]

TO FIND :- Remainder of P(x) ÷ g(x)

SOLUTION

We can solve it by division algorithm as given in the attachment.

But we can go for Remainder Theorem for such questions :-

By remainder Theorem we have to find zero of g(x)

g(x) = x + 3

=> x + 3 = 0

=> x = -3

We have to simply insert the value of x in p(x) to get the remainder :-

P(x) = x^3 - 3x^2 + 3x - 1

p( - 3) = ( - 3)^3 - 3 × (-3)^2 + 3 × -3 -1

= - 27 - 3 × 9 - 9 -1

= - 27 - 27 - 9 -1

= - 64

Hence the remainder is -64.