1. ## Algebra problems

I've got my head stuck around these 2 problems. I'm trying to factor these polynomials, but I just can seem to get them.

The first one is f(x) = x^3 + x^2 - 8x - 6

The 2nd one is f(x) = x^5 + 3x^4 - 4x^3 - 11x^2 - 3x + 2

I'd appreciate any tips, thanks!

2. For the second one, try dividing by a possible root. Try x-2 and/or x+1

If it reduces down, then that's a root and you're on your way.

$\frac{x^{5}+3x^{4}-4x^{3}-11x^{2}-3x+2}{x-2}=x^{4}+5x^{3}+6x^{2}+x-1$

See?. That reduced down to a quartic. Try dividing that by another factor or some other tactic and whittle away at it.

3. Is that the only way to go about factoring these?

4. For 1.

f(-3) = -27 + 9 + 24 - 6 = 0

So (x+3) is a factor of f(x).

By using long division,

f(x) = (x+3) (x^2 - 2x - 2)

Then do factories.

Same for 2.

5. why exactly did you do f(-3) for the first one? where did the -3 come from exactly. Sorry I'm posting on this thread when its not mine but I'm just interested in this problem.

6. Originally Posted by OzzMan
why exactly did you do f(-3) for the first one? where did the -3 come from exactly. Sorry I'm posting on this thread when its not mine but I'm just interested in this problem.
Feel free, this helps me too!

7. Well, it is not exactly f(-3). You’ve to take some values of x, like +1, -1, +2, -2………. After doing some exercise you can easily realize that what is the factor of f(x), without doing any rough.