Question

A treasure chest has a volume of x^3 + 9x^2 + 26x + 24 cm^3 and the height is x + 4 cm. Find the polynomial that would represent the area of the bottom of the treasure chest? Explain your reasoning

Answer 1

\[V=x^3 + 9x^2 +26x +23 =A \times H=A \times (x+4)\]
where V is the volume of the chest
A is the area of the bottom of the chest
H is the height
factor out (x+4) from the V

Answer 2

do you know how to do that?

Answer 3

no

Answer 4

You have to figure out a polynomial that when you multiply it by (x+4) gives you the volume equation above. I do it a little by hit and miss. The polynomial will be in the form of \[ax^2 +bx+c\] and we have to find a, b, and c.

So if I multiply this polynomial by (x+4) I get

\[ax^3+bx^2 +cx+4ax^2+4bx+4c\]
now we combine terms and get\[ax^3 +(b+4a)x^2+(c+4b)x + 4c\]

Answer 5

Now, what must each term, a, b, and c for \[ax^3+(b+4a)x^2+(c+4b)x +4c=x^3+9x^2+26x+24\] a=1
b+4a=9
c+4b=26
4c=24

Answer 6

Can you find a, b, c now?

Answer 7

yes thank you

Answer 8

you are welcome.