1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Doss [256]
1 year ago
11

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

Mathematics
1 answer:
Cloud [144]1 year 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)

You might be interested in
The sum of two numbers is 25. Create an equation using two variables that represents this situation.
dmitriy555 [2]

Answer:

x+y=25

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
What is the slope of a line that is parallel to the line y=3/4x+2
MariettaO [177]
The slope is m=3/4. Hope this helped you with your work let me know if I got the answer correct.
3 0
3 years ago
Read 2 more answers
Faris's gas tank is 1/10 full. After he buys 24 liters of gas, it is 2/5 full. How many liters can Faris's tank hold?
Arisa [49]

Answer:

80 liters

Step-by-step explanation:

24 liters is the difference between 2/5 full and 1/5 full.

Let x = number of liters in full tank.

2/5 x - 1/10 x = 24

4/10 x - 1/10 x = 24

3/10 x = 24

1/10 x = 8

x = 80

Answer: 80 liters

5 0
2 years ago
What is the slope of the line shown?
Anarel [89]

Hello!

\large\boxed{Slope = -\frac{1}{2}}

Use the slope formula along with provided points to solve for the slope.

We can use the points (-4, -1) and (0, -3) and plug these values into the equation:

m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}

m = \frac{-3-(-1)}{0-(-4)} \\\\m = \frac{-2}{4} \\\\m = -\frac{1}{2}

4 0
3 years ago
Read 2 more answers
A mixture of alcohol and water contains a total of 60 oz of liquid there are 12 oz of pure alcohol in the mixture was a percenta
OlgaM077 [116]

Answer:

The mixture contains 80% water and 20% alcohol.

Step-by-step explanation:

Given:

Total Amount of mixture = 60 oz

Amount of alcohol in the mixture = 12 oz

We need to find the percentage of water and percentage of alcohol in the mixture.

Solution:

First we will find the amount of water in mixture.

Now we know that;

Total Amount of mixture is equal to sum of Amount of alcohol in the mixture and amount of water in mixture.

so we can say that;

amount of water in mixture = Total Amount of mixture - Amount of alcohol in the mixture

amount of water in mixture = 60-12 =48\ oz

Now we will find the Percentage amount of water.

Percentage amount of water can be calculated by dividing amount of water in mixture by Total Amount of mixture and then multiplying by 100.

framing in equation form we get;

Percentage amount of water = \frac{48}{60}\times 100 = 80\%

Percentage amount of alcohol = 100\%-80\%=20\%

Hence The mixture contains 80% water and 20% alcohol.

7 0
3 years ago
Other questions:
  • What is the range of Variable B? Scatter plot on a first quadrant coordinate grid. The horizontal axis is labeled Variable A. Th
    11·1 answer
  • Which number is the largest? <br> 1.2 × 10^4<br> 4.5 × 10^−3<br> 3.8 × 10^3 <br> 7.5 × 10^3
    9·1 answer
  • How many solutions does this system
    8·1 answer
  • The expression of 536 × 34​
    11·1 answer
  • The figure consists of two quarter circles and a square.
    10·2 answers
  • Jodi drew the Eiffel Tower 6.5 inches tall. she thought it was too tall so she multiplied its height by 0.8. the second drawing
    8·1 answer
  • This is the graph of f(x)= -6 * 2x. What is the horizontal asymptote
    15·1 answer
  • (PLEASE HELP!!! DUE 4:30!!!)<br> Image of the problem is attached.
    11·1 answer
  • 2. Find the magnitude and direction of the resultant vector of two forces. The first force is 250 pounds at an angle of 25 degre
    15·1 answer
  • Please help me answer number 2.
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!