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
Sloan [31]
3 years ago
8

I don’t understand :(

Mathematics
1 answer:
viktelen [127]3 years ago
4 0

Answer:

The quotient when x^3-4x^2-8x+8 is divided by x+2 is x^2-6x+4 with no remainder, so x+2 is a factor of p(x).

Step-by-step explanation:

As the question suggests, there are two ways to solve this problem: long division (which can always be used to divide polynomials), and synthetic division (which can only be used when you are dividing by something of the form (x-a). In this case, we may use synthetic division, since x+2 is equal to x-(-2). I will use synthetic division here as it is slightly faster than long division.

The -2 on the left represents that we are dividing by x-(-2), and the rest of the numbers in the top row are the coefficients of p(x): 1, -4, -8, and 8.

The first step in synthetic division is to being down the leading coefficient of the polynomial: in this case, the 1 (as indicated in red). Now, we multiply the 1 by -2. We get -2, which we place directly below the -4.

Next, we add directly down the column, (-4 + (-2) is equal to -6), and this answer is placed in the box below. We can continue this process, getting the coefficients 1, -6, 4, and 0 in the bottom row.

This is the answer: the quotient is x^2-6x+4, and the remainder is zero (which indicates that x+2 is a factor of p(x)).

--

Edit: long division

We may also solve this problem using long division (see the second image). The first step is to look at the leading coefficients: since x \times x^2 is equal to x^3, the first term in the quotient will be x^2. Since x^2 \times (x+2) is equal to x^3+2x^2, we must now subtract that from x^3-4x^2-8x+8.

We repeat the same process, as shown in the image. Since we eventually get to zero, the remainder is zero, and the polynomial at the top (x^2-6x+4) is the quotient.

<em>I know this might be difficult to follow, so please comment if you have any questions.</em>

You might be interested in
Review the steps of the proof.
lana [24]

Answer:

steps 2 and 3 must be switched

Step-by-step explanation:

e2020

7 0
2 years ago
Read 2 more answers
To convert a percent to a fraction, which of the following is not done?
slavikrds [6]
What you do, to convert a percention to a fraction is to divide the percent by 100. This will give you the fraction of that percent. Knowing this, you can eliminate all the other possible answers that have been listed.
4 0
3 years ago
A slow boat to china travels at a constant speed of 17.25 miles per hour for 200 hours. how far was the voyage?​
tensa zangetsu [6.8K]

Answer:

3450 miles

Step-by-step explanation:

Multiply the number 17.25 by 200 since the boat is traveling for 200 hours and each hour is 17.25 miles to get 3450 miles which is your answer.

4 0
3 years ago
Read 2 more answers
5) Which one of the following proportions is NOT true?*
Tpy6a [65]
The second one, 69/24 = 23/8 and cannot be simplified further
6 0
3 years ago
Help me quick please --4x-7-3x+4=25
V125BC [204]

Answer:

<h2><em><u>x</u></em><em><u> </u></em><em><u>=</u></em><em><u> </u></em><em><u>32</u></em></h2>

Step-by-step explanation:

4x - 7 - 3x + 4 =25

=> 4x - 3x = 25 + 7

=> <em><u>x = 32 (Ans)</u></em>

3 0
3 years ago
Read 2 more answers
Other questions:
  • This data set shows the weight, in pounds, of six family members.
    7·1 answer
  • In the diagram, point O is the center of the circle and mADB = 43°. If mAOB = mBOC, what is mBDC?
    8·2 answers
  • PLEASE I NEED HELP ASAP! Determine if 9x2 - 42x + 49 can be the area of a square. If so, what would the value of x have to be if
    10·1 answer
  • What is the greatest common factor of 25 and 30
    11·2 answers
  • A line contains the points (3, –2) and (–6, –8). Write the equation of the line using point-slope form.
    12·1 answer
  • There are 36 students in the cafeteria 28 girls and 8 boys. What is the ratio of girls to boys in the cafeteria?
    6·1 answer
  • One angle of a triangle measures 132°. The other two angles are congruent. Enter and solve an equation to find the measure x of
    6·1 answer
  • Plz plz help me with question 3.You will get 15 points and a branliest.
    5·1 answer
  • Addison is paid $40 for tutoring. She spends $16.83 on dinner. How much money does Addison have left and why?
    6·2 answers
  • Find the measure of x.<br> 42°<br> X<br> 17<br> x= [ ?<br> Round to the nearest hundredth.
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!