Question

A polynomial with a degree of 3 that when divided by x+2 has a remainder of -4

Answer 1

P(x)=(x-3)(x-p)(x-q)-4
where p,q are any integers (or even real numbers)

Answer 2

can you write it in a different way; X^3-3^2-4

Answer 3

Choose values of p and q then expand.
Do not forget to add the term "-4".

Answer 4

ok thank you. But I never seen a problem written like that. I dont know how to solve it.

Answer 5

Sorry, the above equation I gave for P(x) is wrong. I took the wrong number. The factor (divisor) should be (x+2), so the revised P(x) is then:
P(x)=(x+2)(x-p)(x-q)-4
you still get to choose integers p and q.

Since (x+2) divides (x+2)(x-p)(x-q) exactly, the remainder is zero for any choice of p and q.
By adding on -4, we make sure the remainder is -4 as required.

Answer 6

ok thank you

Answer 7

You're welcome! :)