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
Kaylee tell Aimee that the shape is a stop sign has a least one right angle. Aimee says that three are no right angles.who is ri
damaskus [11]
Aimee is correct because a stop sign is an octogon. Octogons contain only obtuse angles.
4 0
3 years ago
Name two integers whose quotient is -7
Andrei [34K]

Answer:

1 and -7

Step-by-step explanation:

3 0
3 years ago
What is the answer please help me no links
Elan Coil [88]

Answer:

C= 2.18x + 2.39

Step-by-step explanation:

3 0
3 years ago
4 bags of cement do 18m(squared), how many m(squared) can be done with 7 bags ?
Elis [28]
I think 7 bags do 31.5 m squared
4 0
3 years ago
An exponential function with base greater than 1 eventually shows rapid growth. True or false
Stella [2.4K]
True, it keeps getting multiplied by itself more and more
7 0
2 years ago
Other questions:
  • What number do you subtract from 3 to get 10?
    8·2 answers
  • WILL GIVE BRAINLIEST IF CORRECT!!
    11·1 answer
  • Which expression is equivalent to (18x + 9k) + (2x + 6k)?
    11·2 answers
  • 10. how does the stranger show that he is more aggressive than henry when interacting with elisa at her garden? a. he refuses to
    12·2 answers
  • Find the simple interest.
    12·1 answer
  • What’s the answer????
    11·2 answers
  • Can someone please help me with math.
    10·1 answer
  • The ratio of boys to girls in a class is 7:5. There are 36 students in the class. How many
    6·2 answers
  • Solve for x.<br><br> 0.5x+78.2=287
    7·1 answer
  • For every 15 students there are 3 teachers in the school. Based on this information, about how many teachers are in a school wit
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!