Question

Divide p(x)=x^4+6x^3+7x^2-6x-8 by x+4. What is the remainder

Answer 1

Use the remainder theorem; dividing a polynomial
`p(x)` by
`x-c` leaves a remainder equal to
`p(c)`. Here

`p(x)=x^4+6x^3+7x^2-6x-8`

`\implies p(c)=(-4)^4+6(-4)^3+7(-4)^2-6(-4)-8=\boxed{0}`