Consider the following polynomials over Z_{8} where a is written

hadejada7x

hadejada7x

Answered question

2022-01-14

Consider the following polynomials over Z8 where a is written for [a] in Z8:-
f(x)=2x3+7x+4,g(x)=4x2+4x+6,h(x)=6x2+3.
Find each of the following polynomials with all coefficients in Z8,
f(x)+g(x)

Answer & Explanation

puhnut1m

puhnut1m

Beginner2022-01-15Added 33 answers

Step 1
Given :
The given polynomials over Z8 are
f(x)=2x3+7x+4,g(x)=4x2+4x+6
Compute f(x)+g(x) over Z8
Step 2
f(x)+g(x)=(2x3+7x+4)+(4x2+4x+6)
=8x5+8x4+12x3+28x3+28x2+42x+16x2+16x+24
=0+0+4x3+4x3+4x2+2x+0+0+0
=0+0+0+4x2+2x+0+0+0
=4x2+2x
scomparve5j

scomparve5j

Beginner2022-01-18Added 38 answers

We need to find f(x)+g(x) of the following polynomials f(x)=2x3+7x+4,g(x)=4x2+4x+6, with all coefficients in Z8.
If f(x)=i=0naixi and g(x)=i=0mbixi in R[x], we define addition in R[x] by f(x)+g(x)=i=0k(ai+bi)xi,
where k is the larger of the tow integers n, m.
Thus, we have
f(x)+g(x)=(2x3+7x+4)+(4x2+4x+6)
=(2+0)x3+(0+4)x2+(7+4)x+(4+6)
=2x3+4x2+11x+10
Now, we have
[11]8=[3]8 and [10]8=[2]8.
Thus, we get
f(x)+g(x)=2x3+4x2+3x+2.
Hence, f(x)+g(x)=2x3+4x2+3x+2.
alenahelenash

alenahelenash

Expert2022-01-24Added 556 answers

Given, f(x)=2x3+7x+4,g(x)=4x2+4x+6 Step 2 Now, f(x)+g(x)=(2x3+7x+4)+(4x2+4x+6) =2x3+4x2+(7x+4x)+(4+6) =2x3+4x2+11x+10 Now, [11]8=[3]8 & [10]8=[2]8 Therefore, f(x)+g(x)=2x3+4x2+3x+2

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