1.A mysterious box is delivered to the dinner party you are attending. The label on the box says that the volume of a box is the function f(x) = x3 + 3x2 – 10x – 24. To open the box, you need to identify the correct factors of f(x). Partygoers offer up solutions, and it is your job to find the right ones.

Their suggestions are:
•(x – 1)
•(x + 2)
•(x – 3)
•(x + 4)
•(x + 6)
•(x – 12)

List the correct factors. Then justify your selections with complete sentences.

my factors are x+2, x-3, and x+4, but can someone please help me put those in complete sentences?

Question

1.A mysterious box is delivered to the dinner party you are attending. The label on the box says that the volume of a box is the function f(x) = x3 + 3x2 – 10x – 24. To open the box, you need to identify the correct factors of f(x). Partygoers offer up solutions, and it is your job to find the right ones. 


Their suggestions are:
•(x – 1)
•(x + 2)
•(x – 3)
•(x + 4)
•(x + 6)
•(x – 12)


List the correct factors. Then justify your selections with complete sentences.

my factors are x+2, x-3, and x+4, but can someone please help me put those in complete sentences?

aaronq · Answer

Do you have to explain how you arrived at them, or how to show that they are correct?

anonymous · Answer

you have to explain how you got those answers

aaronq · Answer

Hm, it seems that you would just describe what you did. Is that not sufficient?

anonymous · Answer

yes, but i'm not very good, like when I just try to explain it the words just won't come out :( like it doesn't make sense, and when I try to explain step by step, it all comes out to be like an essay :l

aaronq · Answer

haha well i think an essay should be just fine. It seems like that is exactly what they are asking for. Are you concerned because there is a word limit or something?

anonymous · Answer

not really lol :3 but this is what I have so far The roots must be factors of 24. Because the numbers 3 and -10 are relatively small, the most probable roots would be -4, -3, -2, -1, 1, 2, 3, or 4 
 Use synthetic division and find that the smallest root is -3, So you can now rewrite it as 
 (x + 3)(x^2 - 6x + 8) 
 The second factor can be factored as (x - 2)(x - 4) 
 So the factored form is (x - 3)(x + 2)(x - 4) 
 and the roots are -3, 2, and 4

anonymous · Answer

I know I messed up somewhere for sure because to me it doesn't make sense

aaronq · Answer

It's fine. you just need to clean up your sentences. I would change it to

The roots must be factors of 24. Because the numbers 3 and -10 are relatively small, the most probable roots would be -4, -3, -2, -1, 1, 2, 3, or 4.
Using synthetic division, one can find that the smallest root is -3. It can now be rewritten as  (x + 3)(x^2 - 6x + 8). The quadratic can now be factored as (x - 2)(x - 4) and further factored as (x - 3)(x + 2)(x - 4). The roots, -3, 2, and 4, are solved for by allowing each factor to be equal to zero.

anonymous · Answer

oh ok ^_^ thank you so much!! :)

aaronq · Answer

no problem!