How to solve (6x^4+30x^3+3x+14) / (x+5) in long division. I understand synthetic but not long divison
Long division is a more tedious method compared to synthetic division, but it is still an effective way to divide polynomials. Here are the steps to divide (6x^4+30x^3+3x+14) by (x+5) using long division:
Step 1: Write the dividend (the polynomial being divided) in descending order of exponents. If any term is missing, write a placeholder. In this case, the dividend is already in descending order, so we don't need to do anything.
6x^4 + 30x^3 + 0x^2 + 3x + 14
Step 2: Write the divisor on the left side of the long division symbol.
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x + 5 | 6x^4 + 30x^3 + 0x^2 + 3x + 14
Step 3: Divide the first term of the dividend (6x^4) by the first term of the divisor (x) to get 6x^3. Write this above the long division symbol, directly above the second term of the divisor (5x).
6x^3
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x + 5 | 6x^4 + 30x^3 + 0x^2 + 3x + 14
Step 4: Multiply the divisor by the quotient (6x^3) and write the result below the first two terms of the dividend.
6x^3
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x + 5 | 6x^4 + 30x^3 + 0x^2 + 3x + 14
- (6x^4 + 30x^3)
0x^3
Step 5: Bring down the next term of the dividend (0x^2) and write it beside the remainder. The new dividend is 0x^3 + 3x + 14.
6x^3
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x + 5 | 6x^4 + 30x^3 + 0x^2 + 3x + 14
- (6x^4 + 30x^3)
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0x^3
0x^3 + 3x
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Step 6: Repeat steps 3 to 5 until there are no more terms to bring down. The final quotient is the sum of all the quotients found in step 3.
The final answer is:
6x^3 + 3 - (17/(x+5))
Therefore, (6x^4+30x^3+3x+14) / (x+5) = 6x^3 + 3 - (17/(x+5))
arth’s supply of fossil fuels—oil, coal, and natural gas—is being depleted because of constant use. We depend on fossil fuels to generate electricity and heat. Over millions of years, these valuable resources formed from the remains of buried plants and animals. But we are burning them far faster than nature will ever replace them. Processing and using fossil fuels also produces pollution.
Conserving energy addresses these problems. It preserves fossil fuels for future generations. It also reduces their harmful effects on the environment. It is important to find alternative energy sources to power the electrical devices that we rely on daily.
Energy conservation takes two forms. First, alternatives to fossil fuels are being employed. The best alternatives are renewable. That is, they replenish themselves as we use them. Solar energy is a good example. Second, people are finding ways to reduce their energy use.
Alternative fuels avoid some or all of these problems. Some rely on natural forces such as geothermal heat, sunlight, wind, or water. Most of these alternative sources of energy are environmentally friendly since they do not cause pollution.
Geothermal Energy
Earth’s interior is extremely hot. In places, this heat produces steam near the surface. This steam can be used to heat homes and generate electricity. Geothermal heat produces cheap electricity and little pollution. But it is limited to places that have natural reservoirs of underground steam. They include northern California, Iceland, Italy, and New Zealand.
Solar Energy
The Sun constantly radiates more energy than we could ever use. The challenge is to collect, store, and use this energy in an affordable way. Some solar-energy systems generate electricity. Others produce heat. The good news is that solar technology is improving rapidly. Today, millions of homes and businesses use solar energy. Power companies are also tapping into this limitless energy source.
Wind Energy
People have used windmills for hundreds of years. Early windmills turned wheels to grind grain or pump water. Most modern windmills generate electricity. Like solar technology, wind generators are getting more efficient. Large windmills called wind generators produce electricity on a large scale. They are most useful in places with strong, fairly constant winds.
Water Energy
Hydroelectric power is electricity produced by flowing water. Inside a dam, flowing water turns turbines (like a fan’s blades) to generate electricity. In the past, water wheels were used by mills to grind grain into flour.
Biomass Energy
Biomass fuels such as wood, leaves, food wastes, and manure are made from living things. Biomass materials can be burned as fuels themselves or converted into other fuels, such as gasohol, a mix of alcohol and gasoline.
Answer questions 1 - 4 based on the reading passage above.
1. According to the reading passage above, which is not listed as an alternative energy source?
*
1 point
Geothermal
Solar
Wind
Fossil Fuels
2. What would be a reason to use geothermal energy?
*
1 point
It can be used to produce cheap electricity and it produces little pollution.
It can be found everywhere on earth.
It produces air pollution.
It is expensive.
3. Which alternative energy source is used in millions of homes and businesses?
*
1 point
geothermal energy
solar energy
wind energy
hydroelectric (water) energy
4. Which alternative energy source is best used in places that have strong, fairly constant winds?
*
1 point
Geothermal
Solar
Wind
Water
1. Fossil Fuels
2. It can be used to produce cheap electricity and it produces little pollution.
3. Solar energy
4. Wind
There are many different ways for alternative energy to be used in a house. One way is to generate electricity by collecting the sun's light. To do this, solar panels that change the sunlight into electricity are placed on the roof of the house. The heat from the sun can also be used to heat water that can provide hot water for showers, etc...
Harnessing the power of the wind is another way to make electricity. The wind can turn a large wind turbine (this looks like a fan) which turns a generator that produces electricity.
Using water that flows over a dam is a renewable form of energy that can make electricity to power a house. A large amount of fast moving water that can turn a turbine is needed to generate hydroelectricity. The house would need to be located next to a river to capture this type of energy.
Figure 1
5. The rectangular blue structures on the roof of the house, labeled with the letter "A" seen in Figure 1 are used to turn the sunlight into electricity. They are called
*
1 point
wind turbines
a hydroelectric dam
solar panels
a geothermal energy plant
Figure 2
6. The structure in Figure 2 labeled with the letter "B"
*
1 point
can capture the sunlight to make electricity.
will turn when the wind blows and can generate electricity.
is a source of nuclear energy.
uses geothermal energy to make electricity.
7. In the previous examples, the house of the future will use a form of clean renewable energy. Why is it better to use these types of renewable energy?
*
1 point
The energy is cheap to produce
The energy generates large amounts of carbon dioxide
The energy does not create air pollution
The energy produces waste easily disposed of in a sanitary landfill
8. To make hydroelectricity, you must have
1 point
moving water
wind
sunlight
uranium
5. Solar panels
6. Will turn when the wind blows and can generate electricity.
7. The energy does not create air pollution
8. Moving water
One alternative source of energy that does not produce air pollution is nuclear power. Nuclear power generates 20 percent of electricity in the United States and more than 70 percent of electricity in France. Nuclear power works through nuclear fission, which refers to the splitting of an atom’s nucleus into two nuclei.
To harness electricity from nuclear energy, uranium atoms are split in the process of nuclear fission. Martin Heinrich Klaproth first discovered the element uranium in 1789. He named the element after the planet Uranus, which had been discovered eight years earlier by William Herschel. The element uranium is commonly used because it splits easily.
In a nuclear power plant, the heat released from fission reactions is used to turn water into steam. The steam then turns the blades of a turbine to generate electricity. Water or another fluid pumped through the reactor is heated by the reactions. It passes through a heat exchanger.
Nuclear energy has two main drawbacks. Accidents at nuclear plants have led to safety concerns, and scientists have yet to find safe ways to store dangerous radioactive wastes for thousands of years.
Figure 3
Using Figure 3, what is the last part in making nuclear energy?
1 point
the reactor
the generator
the condenser
the turbine
10. Heat produced by the fission reaction is used to generate steam which turns
*
1 point
the reactor
the blades of the turbine
the cooling tower
the heat exchanger
11. This element is used in nuclear reactors because it splits easily?
*
1 point
uranium
plutonium
radon
strontium
12. Nuclear power while it does not produce air pollution, it does create this toxic item?
*
1 point
carbon dioxide
methane
radioactive waste
radon gas
9. The turbine
10. The blades of the turbine
11. Uranium
12. Radioactive waste