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:

$\frac{16z^{4}-1}{z+1}$

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.