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Created By : Rina Nayak

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Last Updated : Apr 19, 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 5x^6-3x^3+8 by x+1 using Remainder Theorem.

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

Remainder Theorem
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How to Find Remainder of 5x^6-3x^3+8 by x+1 using Remainder Theorem?

Let p(x) = 5x^6-3x^3+8

The zero of x+1 is = -1.

So after P(x) is divided by x+1 we get the remainder i.e. P(-1).

Now, p(-1) = 5x^6-3x^3+8 .

= (8)+(-3.x^3)+(5.x^6)

By putting x = (-1) we can rewrite it as

= (8)+(-3.(-1)^3)+(5.(-1)^6)

= (8)+(3)+(5)

= 16

∴The remainder of given polynomial is 16.

FAQs on Remainder Theorem of 5x^6-3x^3+8 by x+1

1. What is the remainder of 5x^6-3x^3+8 by x+1?

The Remainder of 5x^6-3x^3+8 divided by x+1 is 16.


2. How to Find Remainder of 5x^6-3x^3+8 by x+1 using Remainder Theorem?

Consider x+1 = 0 so that x = -1.

Substitute x = -1 in expression 5x^6-3x^3+8 to get the remiander

Thus, 5x^6-3x^3+8 divided by x+1 remainder is 16.


3. Where can I obtain detailed solution steps for Remainder Theorem of 5x^6-3x^3+8?

The detailed steps for the Remainder Theorem of 5x^6-3x^3+8 are compiled exclusively on our output page.