DIVIDING of POLYNOMIALS?

Question

This is the question:

http://img243.imageshack.us/img243/3426/poy12xv8.png

What is it asking? How can I solve it?

Answer 1

You're given a polynomial P(x), and are asked to factor it, so that you can write it in the form of (x + a)(x^2 + bx + c). So what are the values of a, b and c for which this will work?

One way to find this is to multiply out the expression
(x + a)(x^2 + bx + c). The match the coefficients you get with the original equation. So first, we have:
(x + a)(x^2 + bx + c) =
x(x^2 + bx + c) + a(x^2 + bx + c) =
(x^3 + bx^2 + cx) + (ax^2 + abx + ac) =
x^3 + bx^2 + ax^2 + cx + abx + ac =
(x^3) + (b+a)(x^2) + (c+ab)x + ac

This has to match P(x) = x^3 + 3x^2 + 7x + 10. Notice that this can only happen if (b+a) = 3, (c+ab) = 7, and ac = 10. You now have three equations with three unknowns to solve for. So solve them for a, b, and c.

Answer 2

You are trying to factor the cubic into two multiples, (x+a) and x^2+bx+c. The cubic is x^3+3x^2+7x+10. As a hint, a x c =10 and b+a=3,
and c+ab = 7. You can either solve these equations for a or do a trial and error division to see what works. Actually, what works is (x+2)(x^2+x+5)