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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 5x^3+x^2+x-9 by x+7 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^3+x^2+x-9 by x+7 using Remainder Theorem?

Let p(x) = 5x^3+x^2+x-9

The zero of x+7 is = -7.

So after P(x) is divided by x+7 we get the remainder i.e. P(-7).

Now, p(-7) = 5x^3+x^2+x-9 .

= (-9)+(x)+(x^2)+(5.x^3)

By putting x = (-7) we can rewrite it as

= (-9)+((-7))+((-7)^2)+(5.(-7)^3)

= (-9)+(-7)+(49)+(-1715)

= -1682

∴The remainder of given polynomial is -1682.

FAQs on Remainder Theorem of 5x^3+x^2+x-9 by x+7

1. What is the remainder of 5x^3+x^2+x-9 by x+7?

The Remainder of 5x^3+x^2+x-9 divided by x+7 is -1682.


2. How to Find Remainder of 5x^3+x^2+x-9 by x+7 using Remainder Theorem?

Consider x+7 = 0 so that x = -7.

Substitute x = -7 in expression 5x^3+x^2+x-9 to get the remiander

Thus, 5x^3+x^2+x-9 divided by x+7 remainder is -1682.


3. Where can I obtain detailed solution steps for Remainder Theorem of 5x^3+x^2+x-9?

The detailed steps for the Remainder Theorem of 5x^3+x^2+x-9 are compiled exclusively on our output page.