Question

The work below shows division of a polynomial by a binomial using long division.



What is the remainder?

–16
–8
8
16

Answer 1

I don't see the polynomial/divisor or the long-division work — can you paste the expression or upload the image?

If you want to find the remainder quickly: use the Remainder Theorem. If the divisor is x − c (or any linear ax + b), the remainder equals f(c) where c is the root of the divisor (for ax + b, c = −b/a). So:

- divisor x − 2 → remainder = f(2)
- divisor x + 4 → remainder = f(−4)
- divisor 2x − 1 → remainder = f(1/2)

Give me the polynomial and the binomial and I’ll compute which of −16, −8, 8, 16 is the remainder.