SOLUTION: The average speed of a car is 2x^2 + 8k - 12 km/h. How far can it go in 3x-2 hours?

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Question 1190851: The average speed of a car is 2x^2 + 8k - 12 km/h. How far can it go in 3x-2 hours?
Found 2 solutions by Edwin McCravy, math_tutor2020:
Answer by Edwin McCravy(20059)   (Show Source): You can put this solution on YOUR website!

"Rate" means "speed"

Distance =    rate    x time
    |           |     |   |
    |           |     |   |
    v           v     v   v
    ?    = (2x2+8x-12)∙(3x-2)

Multiply that out.

Edwin
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

I'm assuming you mean to say 8x instead of 8k
The idea is to multiply the speed with the time value to find the distance.

distance = rate*time
distance = speed*time

So the goal is to multiply out (2x^2+8x-12)*(3x-2)

One way to multiply polynomials is to lay out a table like this
2x^28x-12
3xABC
-2DEF
The letters A through F are placeholders for something else.

To figure out what that "something else" is, we multiply the outer pair of items.
So the upper left corner is 6x^3 because 3x times 2x^2 = 6x^3
This means we replace the "A" with 6x^3
2x^28x-12
3x6x^3BC
-2DEF


The bottom right corner is 24 because -2*(-12) = 24
Therefore, we replace the letter F placeholder with 24
2x^28x-12
3x6x^3BC
-2DE24


The other items are handled in a very similar fashion.

I'll let you fill out the rest of the table.
Once the table is fully complete, you add up the stuff found inside.
If there are any like terms, make sure to combine them.

For more information, check out the box method.

A similar example is shown below.

-----------------------------

Example:

Let's say we wanted to multiply x^2+5x+6 with x-3

The starting table looks like
x^25x6
xABC
-3DEF


Then we have
A = x*x^2 = x^3 in the upper left corner
B = x*5x = 5x^2
C = x*6 = 6x
to finish off the first row.

For the next row, we have,
D = -3x^2
E = -3*5x = -15x
F = -3*6 = -18

This is the completed table for this example
x^25x6
xx^35x^26x
-3-3x^2-15x-18
Notice that any given row is the result of distributive property. Eg: Row 1 has x*(x^2+5x+6) = x^3+5x^2+6x

Then we add up the stuff found in the table (items A through F earlier)
A+B+C+D+E+F = x^3+5x^2+6x+(-3x^2)+(-15x)+(-18) = x^3+2x^2-9x-18

Note we added these two pairs of like terms
5x^2 and -3x^2 to get 2x^2
6x and -15x to get -9x

Therefore,
(x-3)*(x^2+5x+6) = x^3+2x^2-9x-18
This is of course an example and not the final answer to your particular question. However, you will follow the same type of steps.
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