If the polynomial 6x6 – 4x5 + 9x – 6 is to be factored by grouping, which step should be taken?

1 answer:

3 0

I think you're trying to say 6x^6-4x^5+9x-6. ^ Is a symbol that means the number after it is an exponent.
First step, find the gcf (greatest common factor) between the first two parts. The gcf of 6x^6-4x^5 is 2x^5.
Now take it out. You get
2x^5(3x-2)
If you expand that equation, you will get 6x^6-4x^5 which is why you know it's correct.
Now do the same for the second half.
The gcf for the second two parts is 3.
3(3x-2)
Notice anything? Yep, in both of them, after you take out the gcf, you get (3x-2)
Now, you combine them into one equation
2x^5(3x-2)+3(3x-2)
Then you do this
(2x^5+3)(3x-2)
That's your factored form.

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Answer:

Part A)

The height of the water level in the rectangular vessel is 2 centimeters.

Part B)

4000 cubic centimeters or 4 liters of water.

Step-by-step explanation:

We are given a cubical vessel that has side lengths of 10cm. The vessel is completely filled with water.

Therefore, the total volume of water in the cubical vessel is:

$V_{C}=(10)^3=1000\text{ cm}^3$

This volume is poured into a rectangular vessel that has a length of 25cm, breadth of 20cm, and a height of 10cm.

Therefore, if the water level is h centimeters, then the volume of the rectangular vessel is:

$V_R=h(25)(20)=500h\text{ cm}^3$

Since the cubical vessel has 1000 cubic centimeters of water, this means that when we pour the water from the cubical vessel into the rectangular vessel, the volume of the rectangular vessel will also be 1000 cubic centimeters. Hence:

$500h=1000$

Therefore:

$h=2$

So, the height of the water level in the rectangular vessel is 2 centimeters.

To find how how much more water is needed to completely fill the rectangular vessel, we can find the maximum volume of the rectangular vessel and then subtract the volume already in there (1000 cubic centimeters) from the maximum volume.

The maximum value of the rectangular vessel is given by :

$A_{R_M}=20(25)(10)=5000 \text{ cm}^3$

Since we already have 1000 cubic centimeters of water in the vessel, this means that in order to fill the rectangular vessel, we will need an additional:

$(5000-1000)\text{ cm}^3=4000\text{ cm}^3$