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Doss [256]
11 months ago
11

I have a question about polynomial division it is in the picture

Mathematics
1 answer:
Cloud [144]11 months ago
4 0

To answer this question, we have to do the long division process for polynomials. We can do the operation as follows:

To do this division process, we have:

1. Divide the first term of the dividend by the first element of the divisor. They are:

\frac{-4x^3}{4x^2}=-x

2. Now, we have to multiply this result by the divisor, and the result will change its sign since we have to subtract that result from the dividend as follows:

-x\cdot(4x^2_{}-4x-4)=-4x^3+4x^2+4x

And since we to subtract this result from the dividend, we end up with:

-(-4x^3+4x^2+4x)=4x^3-4x^2-4x

3. Then we have the following algebraic addition:

\frac{\begin{cases}-4x^3+24x^2-15x-15 \\ 4x^3-4x^2-4x\end{cases}}{20x^2-19x-15}

4. Again, we need to divide the first term of the dividend by the first term of the divisor as follows:

\frac{20x^2}{4x^2}=5

5. And we have to multiply 5 by the divisor, and the result will be subtracted from the dividend:

5\cdot(4x^2-4x-4)=20x^2-20x-20

Since we have to subtract this from the dividend, we have:

-(20x^2-20x-20)=-20x^2+20x+20

6. And we have to add this algebraically to the dividend we got in the previous step:

\frac{\begin{cases}20x^2-19x-15 \\ -20x^2+20x+20\end{cases}}{x+5}

And this is the remainder of the division, x + 5.

As we can see from the division process, we got as:

1. The quotient: -x + 5

q=-x+5

2. The remainder: x + 5.

R=x+5

Since we have that the dividend = divisor * quotient + remainder.

Therefore, the result for this division is:

-4x^3+24x^2-15x-15=(4x^2-4x-4)\cdot(-x+5)+(x+5)

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Answer:

32

Step-by-step explanation:

The formula needed to solve this question by hand is:

x^{\frac{m}{n}} =\sqrt[n]{x^{m}}

256^(5/8) = 8th root of 256^5

256^(5/8) = 8th root of 1280

<u>256^(5/8) = 32</u>

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C

Step-by-step explanation:

Total Work hours = 3 1/2 hours

One routine physical routine requires: 1/3 hours.

Number of routines can be completed = Total work hours / Time required for one physical routine

= 3\frac{1}{2}  / \frac{1}{3}\\=\frac{7}{2} /\frac{1}{3} \\=\frac{7}{2} *3\\

= 10.5 routines.

In this case, we are unable to complete half a routine (0.5), so we will choose the highest possible whole number, in this case, its 10 routines.

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a garden table and a bench cost $1,025 combined the garden table cost $75 more than the bench what is the cost of the bench
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Anne is painting her house light blue. To make the color she wants, she must add 3 cans of white paint to every 2 cans of blue p
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Answer:

9 cans of white paint

Step-by-step explanation:

To solve this you can set up a ratio.

The ratio right now is 3 : 2, you have 3 cans of white paint for every 2 cans of blue paint. This question is asking how many white paint cans would be needed for 6 cans of blue paint. You can see the relationship between the number of blue paint cans and the new number of blue paint cans, maybe it's multiplying by 4 or 2 for example, and once we find that out we can do the same exact thing to the white cans.

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We can see that to get from 2 to 6 you multiply by 3, so now we do that to the other side of the fraction as well, we multiply by 3. 3 multiplied by 3 is 9, so if we were to have 6 cans of blue paint we would need 9 cans of white paint to get that perfect shade of light blue. Anne would need 9 cans of white paint if she had 6 cans of blue paint to make her shade of blue.

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3 years ago
Consider two circular swimming pools. Pool A has a radius of 48 feet, and Pool B has a diameter of 29.46 meters. Complete the de
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Answer: pool B has a greater circumference.

Step-by-step explanation:

The formula for determining the circumference if a circle is expressed as

Circumference = 2πr

Where

r represents the radius of the circle.

π is a constant whose value is 3.14

Pool A has a radius of 48 feet.

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Radius of pool B = 29.46/2 = 14.73 meters

The circumference of pool B is

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Therefore, pool B has a greater circumference.

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