Question

When p(x)=2x^4+kx+1 is divided by x+1, the remainder is the same as when q(x)=3x^4+kx^2+2 iis divided by x-1. Find k

Answer 1

k = -1

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