Question

Determine the remainder when (5x3 + 49x2 + 74x + 6) is divided by (x + 8).

Answer 1

The polynomial remainder theorem says that the remainder when dividing a polynomial
`P(x)` by a linear divisor
`x-k` is simply
`P(k)`.

If
`P(x)=5x^3+49x^2+74x+6`, then the remainder upon dividing by
`x+8` is


`P(-8)=-10`

You could also verify this by actually computing the quotient and remainder.