Question

Use the remainder Theorem to find the remainder for the given division. (16z^4-1)/(z+1)

Answer 1

Remainder Theorem: when a polynomial P(x) is divided by (x - a), the remainder is P(a).

Given expression:

`(16z^(4)-1)/(z+1)`

In this case:

`P(z)=16z^4-1`
`z=-1`

To know the reminder, we have to plug in the value of z in the polynomial:

`P(-1)=16(-1)^4-1`

Simplifying:

`P(-1)=16(1)^{}-1`
`P(-1)=16^{}-1`
`P(-1)=15`

Answer: The remainder is 15.