Division of Polynomials

[devilgenedanny]

Hi, nice to meet everyone, this is my first post and first maths question in this forum. I have a question that I am stuck and do not know what to do.
Here is the question:

When P(x) = ax^3 + bx^2 + cx +d is divided by x + 2, the remainder is -5. Find a possible set of the constants a, b, c and d.

[MAS1]

Originally Posted by devilgenedanny

Hi, nice to meet everyone, this is my first post and first maths question in this forum. I have a question that I am stuck and do not know what to do.
Here is the question:

When P(x) = ax^3 + bx^2 + cx +d is divided by x + 2, the remainder is -5. Find a possible set of the constants a, b, c and d.

One possible answer is:
a = 1
b = 6
c = 11
d = 1

A remainder is what is added (or subtracted) after all of a polynomials factors are divided. I got these by picking P(x) = (x + 1)(x + 2)(x + 3) - 5, but you could just as easily choose (x + 2)(x + 2)(x + 2) - 5, or almost anything else.

From my first choice, then:
P(x) = (x^2 + 3x + 2)(x + 3) - 5
P(x) = (x^3 + 6x^2 + 11x + 6) - 5
P(x) = x^3 + 6x^2 + 11x + 1

Another choice would be:
a = 0
b = 0
c = 1
d = -3
for p(x) = x - 3, since (x - 3) divided by (x + 2) = 1 with remainder -5.

Hope this helps.