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Find Remainder of 6x^4+8x^3+6x^2-4x+27 by x+2 using Remainder Theorem

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 6x^4+8x^3+6x^2-4x+27 by x+2 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 6x^4+8x^3+6x^2-4x+27 by x+2 using Remainder Theorem?

Given values are

f(x) = 6x^4+8x^3+6x^2-4x+27

x = -2.

Given Polynomial is 6x^4+8x^3+6x^2-4x+27 .

= (27)+(-4.x)+(6.x^2)+(6.x^4)+(8.x^3)

By putting x = (-2) we can rewrite it as

= (27)+(-4.(-2))+(6.(-2)^2)+(6.(-2)^4)+(8.(-2)^3)

= (27)+(8)+(24)+(96)+(-64)

= 91

The remainder of given polynomial is 91.

FAQs on Remainder Theorem of 6x^4+8x^3+6x^2-4x+27 by x+2

1. What is the remainder of 6x^4+8x^3+6x^2-4x+27 by x+2?

The Remainder of 6x^4+8x^3+6x^2-4x+27 divided by x+2 is 91.


2. How to Find Remainder of 6x^4+8x^3+6x^2-4x+27 by x+2 using Remainder Theorem?

Consider x+2 = 0 so that x = -2.

Substitute x = -2 in expression 6x^4+8x^3+6x^2-4x+27 to get the remiander

Thus, 6x^4+8x^3+6x^2-4x+27 divided by x+2 remainder is 91.


3. Where can I obtain detailed solution steps for Remainder Theorem of 6x^4+8x^3+6x^2-4x+27?

The detailed steps for the Remainder Theorem of 6x^4+8x^3+6x^2-4x+27 are compiled exclusively on our output page.