# Thread: word problem using polynomials

1. ## word problem using polynomials

hi i need help with this question, i got some of it...

The volume of a cardboard box is $\displaystyle x^3 - 8x^2 + 17x - 10$ Factor this polynomial.

i got (x-1)(x-5)(x-2)

if these factors represent the length, width, and height, find the demensions of a box that has a volume of $\displaystyle 20cm^3$

i got ...
$\displaystyle x^3 - 8x^2 + 17x - 10 = 20$
$\displaystyle x^3 - 8x^2 + 17x - 30 = 0$

i then found a factor of (x-6), and after putting that through senthetic division i was left with $\displaystyle x^2 - 2x + 5$, but this dosent really factor, so i think i've done something wrong...help please

2. Originally Posted by extraordinarymachine
hi i need help with this question, i got some of it...

The volume of a cardboard box is $\displaystyle x^3 - 8x^2 + 17x + 10$ Factor this polynomial.

i got (x-1)(x-5)(x-2)<<< = x^3-8x^2+17x-10

if these factors represent the length, width, and height, find the demensions of a box that has a volume of $\displaystyle 20cm^3$

i got ...
$\displaystyle x^3 - 8x^2 + 17x + 10 = 20$
$\displaystyle x^3 - 8x^2 + 17x\bold{\color{red} - 10} = 0$

i then found a factor of (x-6), and after putting that through senthetic division i was left with $\displaystyle x^2 - 2x + 5$, but this dosent really factor, so i think i've done something wrong...help please
...

3. Originally Posted by earboth
.The volume of a cardboard box is Factor this polynomial.

i got (x-1)(x-5)(x-2)<<< = x^3-8x^2+17x-10

if these factors represent the length, width, and height, find the demensions of a box that has a volume of

i got ...

..
i'm not sure what you did here, or what your trying to say.
the question was actually $\displaystyle x^3 - 8x^2 + 17x - 10$

4. Originally Posted by extraordinarymachine
i'm not sure what you did here, or what your trying to say.
the question was actually $\displaystyle x^3 - 8x^2 + 17x - 10$
I noticed that you have corrected the typo in your first post.

Now all your calculations are OK.

You can't factor $\displaystyle x^2-2x+5$ because this term is greater zero for all $\displaystyle x \in \mathbb{R}$.

5. and here i thought i was wrong lol

6. Originally Posted by extraordinarymachine
and here i thought i was wrong lol
To finish the original question:

You certainly have noticed that you get only one solution: x = 6.

Thus the demensions of the box are 5 * 1 * 4 which yields indeed 20.