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Created By : Rina Nayak

Reviewed By : Rajashekhar Valipishetty

Last Updated : Apr 25, 2023

The Remainder Theorem is an approach to Euclidean polynomial division. According to this theorem, dividing a polynomial P(x) by a factor (x - a), which is not an element of the polynomial, yields a smaller polynomial and a remainder. Here you can check the answer for Find Remainder of x^2-3x+3 by x+3 using Remainder Theorem.

Ex: x^2+2x+1,x+1 (or) x^2-1,x-1 (or) x^3-1,x+1

Remainder Theorem

How to Find Remainder of x^2-3x+3 by x+3 using Remainder Theorem?

Let p(x) = x^2-3x+3

The zero of x+3 is = -3.

So after P(x) is divided by x+3 we get the remainder i.e. P(-3).

Now, p(-3) = x^2-3x+3 .

= (3)+(x^2)+(-3.x)

By putting x = (-3) we can rewrite it as

= (3)+((-3)^2)+(-3.(-3))

= (3)+(9)+(9)

= 21

∴The remainder of given polynomial is 21.

FAQs on Remainder Theorem of x^2-3x+3 by x+3

1. What is the remainder of x^2-3x+3 by x+3?

The Remainder of x^2-3x+3 divided by x+3 is 21.

2. How to Find Remainder of x^2-3x+3 by x+3 using Remainder Theorem?

Consider x+3 = 0 so that x = -3.

Substitute x = -3 in expression x^2-3x+3 to get the remiander

Thus, x^2-3x+3 divided by x+3 remainder is 21.

3. Where can I obtain detailed solution steps for Remainder Theorem of x^2-3x+3?

The detailed steps for the Remainder Theorem of x^2-3x+3 are compiled exclusively on our output page.