Question

The polynomial x^3 + 5x^2 -57x -189 expresses the volume, in cubic inches, of a shipping box, and the width is (x+3) in. If the width of the box is 15 in., what are the other two dimensions? ( Hint: The height is greater than the depth.)

Answer 1

A.) height: 19 in, depth 5 in
B.) h 21 in, d 5 in
C.) h 19 in, d 7 in
D.) h 21 in, d 7 in

Answer 2

@neer2890

Answer 3

factor 189 and find which makes the equation zero.

Answer 4

ok I tried it and got C is that correct??

Answer 5

how did you find it

Answer 6

my teacher helped with part of it and i tried to finish the rest that's hoe i got C, i just wanted to check me answer

Answer 7

you know (x+3) is a factor of \[x ^{3}+5x ^{2}-57x-189=0\]
{if you want to check then put x=-3 in above equation}
now this whole equation can be written as
\[(x+3)(x ^{2}+2x-63)=0\]

Answer 8

we know that (x+3) is the width of box.
so we just have to find the value of x from equation
\[x ^{2}+2x-63=0\]

Answer 9

and we will get the other two dimensions

Answer 10

how do i do that

Answer 11

\[x ^{2}+2x-63=0\]
=(x+9)(x-7)

Answer 12

you can find roots of any quadratic equation \[ax ^{2}+bx+c=0\]
by this formula
\[x=\frac{ -b \pm \sqrt{b ^{2}-4ac} }{ 2a }\]

Answer 13

ok and how do i plug that in?

Answer 14

you will get two values of x as x=-9,7
this indicates that (x+9) and (x-7) are factors of
\[x ^{2}+2x-63=0\]
because if x=9 then x-9=0
and if x=7 then x-7=0

Answer 15

now , we know that x+3=15
so, x=15-3=12
so width of box= 12 inches

Answer 16

similarly, length =(x+9)=12+9=21 inches
and depth= x-7=12-7=5 inches

Answer 17

So B.??

Answer 18

yup...:p

Answer 19

thank you so much, i have another question can you help with that one too ill post it in a new question

Answer 20

ok