Answer:
k = -1
Step-by-step explanation:
Here, we want to get the value of k
Now, to get the remainders, we set the linear factors to zero, solve for x and insert the value of x into the polynomial
for x + 1 = 0
x= -1
insert -1 into p(x)
we have this as;
2(-1)^4 + k(-1) + 1
= 2 - k + 1 = 3-k
for the second
set x-1 to zero
x = 1
insert into q(x)
q(1) = 3(1)^4 + k(1)^2 + 2
= 5 + k
so we can now equate the two remainders;
5 + k = 3-k
k + k = 3-5
2k = -2
k = -2/2
k = -1
