Question

how can i create a polynomial my own third degree polynomial that when divided by x + 2 has a remainder of –4?

Answer 1

Suppose P(x) is your polynomial. If when divided by (x+2) it has a remainder of -4, then that means we can write

P(x) = (x+2)Q(x) - 4

for some other polynomial Q(x).

Hence to answer your question, choose any polynomial Q(x) such that P(x) is third order. That is, make Q(x) an arbitrary second order polynomial.

Answer 2

what would the equation look like when written out?

Answer 3

Well, after you've chosen a Q(x), you can expand it and see. What's the simplest second order polynomial Q(x) you can think of?

Answer 4

i have no idea

Answer 5

What is an example of a second order polynomial?

Answer 6

What's the definition of a nth order polynomial?

Answer 7

A polynomial is a finite sum of monomials, such as
x, 2x, -5x, x^3, -17x^4, etc.

The order of a polynomial is the highest power of x in the monomials. For example
x, -2x, 17x, 5x + 3
are all examples of first order polynomials.

x^2, -3x^2, x^2 + x, x^2 + 5, x^2 - 18x + 25959
are all examples of second order polynomials

x^3 is a third order polynomial, as is (x+1)^3 = x^3 + 3x^2 + 3x + 1

Make sense?

Answer 8

-x^3-3x^2-2x

this is what i got !