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Created By : Rina Nayak

Reviewed By : Rina Nayak

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 -4x^3+5x^2+8 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
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How to Find Remainder of -4x^3+5x^2+8 by x+3 using Remainder Theorem?

Let p(x) = -4x^3+5x^2+8

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) = -4x^3+5x^2+8 .

= (8)+(-4.x^3)+(5.x^2)

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

= (8)+(-4.(-3)^3)+(5.(-3)^2)

= (8)+(108)+(45)

= 71

∴The remainder of given polynomial is 71.

FAQs on Remainder Theorem of -4x^3+5x^2+8 by x+3

1. What is the remainder of -4x^3+5x^2+8 by x+3?

The Remainder of -4x^3+5x^2+8 divided by x+3 is 71.


2. How to Find Remainder of -4x^3+5x^2+8 by x+3 using Remainder Theorem?

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

Substitute x = -3 in expression -4x^3+5x^2+8 to get the remiander

Thus, -4x^3+5x^2+8 divided by x+3 remainder is 71.


3. Where can I obtain detailed solution steps for Remainder Theorem of -4x^3+5x^2+8?

The detailed steps for the Remainder Theorem of -4x^3+5x^2+8 are compiled exclusively on our output page.