Find Remainder of 3x^6+3x^4-3x^2+6 by x+1 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 3x^6+3x^4-3x^2+6 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
How to Find Remainder of 3x^6+3x^4-3x^2+6 by x+1 using Remainder Theorem?
Let p(x) = 3x^6+3x^4-3x^2+6
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) = 3x^6+3x^4-3x^2+6 .
= (6)+(-3.x^2)+(3.x^4)+(3.x^6)
By putting x = (-1) we can rewrite it as
= (6)+(-3.(-1)^2)+(3.(-1)^4)+(3.(-1)^6)
= (6)+(-3)+(3)+(3)
= -3
∴The remainder of given polynomial is -3.
FAQs on Remainder Theorem of 3x^6+3x^4-3x^2+6 by x+1
1. What is the remainder of 3x^6+3x^4-3x^2+6 by x+1?
The Remainder of 3x^6+3x^4-3x^2+6 divided by x+1 is -3.
2. How to Find Remainder of 3x^6+3x^4-3x^2+6 by x+1 using Remainder Theorem?
Consider x+1 = 0 so that x = -1.
Substitute x = -1 in expression 3x^6+3x^4-3x^2+6 to get the remiander
Thus, 3x^6+3x^4-3x^2+6 divided by x+1 remainder is -3.
3. Where can I obtain detailed solution steps for Remainder Theorem of 3x^6+3x^4-3x^2+6?
The detailed steps for the Remainder Theorem of 3x^6+3x^4-3x^2+6 are compiled exclusively on our output page.