Question

pleaseeee helpppp me understand thiss...

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.)

A.
height: 19 in.

depth: 5 in.

B.
height: 21 in.

depth: 5 in.

C.
height: 19 in.

depth: 7 in.

D.
height: 21 in.

depth: 7 in.

Answer 1

divide out the (x+3) from the givin poly and factor the results

Answer 2

or

we can work it more starightforward

(x+3) (ax^2 + bx + c) has to equate to the given poly

multiply it out and compare parts

Answer 3

or, leave it in all factored form, and then multiply

(x+3)(x-h)(x-d) and compare parts .... there are a few approaches to it, but these seem to be the most simplest to comprehend

Answer 4

(x+3) (ax^2 + bx + c)

x(ax^2 + bx + c) +3(ax^2 + bx + c)

ax^3 + bx^2 + cx +3ax^2 + 3bx + 3c

ax^3 + (b+3a)x^2 + (c+3b) x + 3c
1x^3 + 5 x^2 -57 x -189

comparing parts

a=1
c=-189/3 = -63

b+3a = 5, b = 2, since a=1

so our quadratic is:
x^2 +2x -63

does it factor?

Answer 5

9 and -7 are -63, and add to 2

(x+3)(x-9)(x+7) defines the parts, what are the parts when x=12?

Answer 6

+9 an -7 ....

Answer 7

im sorry im still really confused

Answer 8

the roots are the opposite of the dohickies ... got a little confused at the end lol

Answer 9

you have to find someway to determine the quadratic that (x+3) multiplies to to get the stated cubic .. right?

Answer 10

okay right, i get it but im just confused about what to do at the end.