Question

I multiply (x-6) and (x+2) to get x^2+2x-6x-12 then I multiply that by (x+7) and I get x^3+3x^2-40x-84 but I think I'm supposed to be getting x^3+x^2-40x-84. Was my first answer right? @math-geek

Answer 1

@phi

Answer 2

@zepdrix

Answer 3

@iambatman

Answer 4

get x^2+2x-6x-12

that is correct, but not simplified. you have the terms 2x - 6x
that is 2 x's take away 6 x's. How many x's do you have ?

Answer 5

-4x and I got that part. So then I'm left with \[(x+7)x^2-4x-12\]

Answer 6

yes, but with parens
\[ (x+7)(x^2-4x-12) \]

Answer 7

When I simplify, I end up with \[f(x)=x^3+3x^2-40x-84\] but I dont know if that's right

Answer 8

one way to do it is "distribute"
we know
A(x+7) = xA +7A
if A is complicated , this rule still works.
i.e. if A is x^2−4x−12 we get
x(x^2−4x−12) + 7(x^2−4x−12)

now distribute again
x^3 -4x^2 -12x + 7x^2 -28x -84

now combine "like terms"
x^3 + (-4x^2 +7x^2) + (-12x -28x) -84
x^3 +3x^3 -40x -84

Answer 9

that matches your result. Great minds think alike!

Answer 10

Got it!! :) now using my function, I need to answer this question but I'm not sure how to do so.

Using both fundamental Theorem and Descartes` rule of signs, prove to the construction foreman that your funtion matches your graph. Use complete sentences.

Answer 11

Do you have a graph of this function ?

Answer 12

I see houses, but no graph.

Here is a graph, using Geogebra to plot it

Answer 13

Here is the fundamental theorem
http://www.mathsisfun.com/algebra/fundamental-theorem-algebra.html

Answer 14

At the beginning of the problem, it says: As one of the new roller coaster engineers, you have been tasked with developing a roller coaster that will intertwine with existing Oakville Lake Amusement Park structures. For one of the more thrilling sections, the roller coaster will dive down in-between buildings, plummet underground, pop back up, and coast over a hill before shooting back underground. There must be three distinct points where the roller coaster crosses the x–axis. Precise measurements and attention to detail are very important.
And that my graph cannot go through the structures of the houses.

Answer 15

the fundamental theorem says that
x^3 +3x^3 -40x -84
which is an "order 3" polynomial (because the highest exponent is 3)
has 3 "roots" where it crosses the x-axis
(not a surprise, because I assume you picked the 3 zeros)

Answer 16

Descartes rule of signs
tells us a little info about the roots based on the polynomial (the graph, if you have it, tells you a lot more)

see
http://www.purplemath.com/modules/drofsign.htm

Answer 17

Yes, I know it has 3 roots/zeros but I don't get how this helps me find how low the points are going to be. Im so confused lol

Answer 18

the question states
***
Using both fundamental Theorem and Descartes` rule of signs, prove to the construction foreman that your funtion matches your graph. Use complete sentences.
***
examining
x^3 +3x^3 -40x -84
The fundamental Thm tells us there is 3 roots, and this matches the graph.
Descartes' rule of signs tells us (whatever it tells us), which matches the graph.
You have to use that rule (see the link or your notes)

Of course, you have to plot the graph.

Answer 19

neither the fundament thm nor Descartes rule of signs tells us anything about the height of the curve or where it has max or min values. they tell us about the roots (where the curve crosses the x-axis)