Find Remainder of x^4+8x^3+12x^2 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 x^4+8x^3+12x^2 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 x^4+8x^3+12x^2 by x+1 using Remainder Theorem?
Let p(x) = x^4+8x^3+12x^2
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) = x^4+8x^3+12x^2 .
= (x^2)+(x^2 + 8.x + 12)
By putting x = (-1) we can rewrite it as
= ((-1)^2)+((-1)^2 + 8.(-1) + 12)
= (1)+(5)
= 5
∴The remainder of given polynomial is 5.
FAQs on Remainder Theorem of x^4+8x^3+12x^2 by x+1
1. What is the remainder of x^4+8x^3+12x^2 by x+1?
The Remainder of x^4+8x^3+12x^2 divided by x+1 is 5.
2. How to Find Remainder of x^4+8x^3+12x^2 by x+1 using Remainder Theorem?
Consider x+1 = 0 so that x = -1.
Substitute x = -1 in expression x^4+8x^3+12x^2 to get the remiander
Thus, x^4+8x^3+12x^2 divided by x+1 remainder is 5.
3. Where can I obtain detailed solution steps for Remainder Theorem of x^4+8x^3+12x^2?
The detailed steps for the Remainder Theorem of x^4+8x^3+12x^2 are compiled exclusively on our output page.