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
nata0808 [166]
2 years ago
6

MAT 171

Mathematics
1 answer:
steposvetlana [31]2 years ago
5 0

Using the Factor Theorem, the polynomials are given as follows:

1. P(x) = x^5 + 2x^4 - 7x^3 + x^2

2. P(x) = 0.8(x^4 - 4x^3 - 16x^2 + 64x)

3. P(x) = -0.1(x³ - 4x² - 3x + 18)

<h3>What is the Factor Theorem?</h3>

The Factor Theorem states that a polynomial function with roots x_1, x_2, \codts, x_n is given by:

f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)

In which a is the leading coefficient.

Item a:

The parameters are:

a = 1, x_1 = x_2 = 1, x_3 = x_4 = 0, x_5 = -4

Hence the equation is:

P(x) = (x - 1)²x²(x + 4)

P(x) = (x² - 2x + 1)(x + 4)x²

P(x) = (x³ + 2x² - 7x + 1)x²

P(x) = x^5 + 2x^4 - 7x^3 + x^2

Item b:

The roots are:

x_1 = x_2 = 4, x_3 = 0, x_4 = -4

Hence:

P(x) = a(x - 4)²x(x + 4)

P(x) = a(x² - 16)x(x - 4)

P(x) = a(x³ - 16x)(x - 4)

P(x) = a(x^4 - 4x^3 - 16x^2 + 64x)

It passes through the point x = 5, P(x) = 36, hence:

45a = 36.

a = 4/5

a = 0.8

Hence:

P(x) = 0.8(x^4 - 4x^3 - 16x^2 + 64x)

Item 3:

The roots are:

x_1 = x_2 = 3, x_3 = -2

Hence:

P(x) = a(x - 3)²(x + 2)

P(x) = a(x² - 6x + 9)(x + 2)

P(x) = a(x³ - 4x² - 3x + 18)

For the y-intercept, x = 0, y = -1.8, hence:

18a = -1.8 -> a = -0.1

Thus the function is:

P(x) = -0.1(x³ - 4x² - 3x + 18)

More can be learned about the Factor Theorem at brainly.com/question/24380382

#SPJ1

You might be interested in
Please help me please will give brainliest to anyone who is good​
hichkok12 [17]

Answer:

C

Step-by-step explanation:

N = st

Number of toothpicks = (number of students) x (toothpicks)

5 0
3 years ago
Read 2 more answers
Given the radius of a cone is 4 cm and its volume is 134 square cm, which of the following is closest to its height?
Mademuasel [1]

Answer:

7.99

Step-by-step explanation:

Volume of cone =  V=πr^2h/3

134 = π*4^2*x/3

x = 7.99

5 0
3 years ago
One-Half the difference of a number and 15
slega [8]

Answer:

x - 15 ÷ 2

Step-by-step explanation:

Since it wants you to find the half of your answer after you find the difference, be sure to leave the two at the end of your equation. With that said, let's move into finding out what "the difference of a number and fifteen is". Whenever they tell you 'a number', it means they want you to put a variable, such as x, since you do not know the number and it could be any number. Now, the "difference" of something usually means...you guessed it, subtraction! Now that you've decoded your equation, you now know it means that x - 15 is the first part, and you can now put the one half right after it.

If this is confusing, I can explain further. :D

5 0
3 years ago
Read 2 more answers
Which expressions are equivalent to 4x^4-9x^2?
weeeeeb [17]
We can cosider this to be  a difference of 2 squares  so 

4x^4 - 9x^2 = (2x^2 - 3x)(2x^2 + 3x)   so D is one answer

also we could take x^2  out and get 
x^2(4x^2 - 9)  = C
3 0
3 years ago
A punch recipe that serves 24 people calls for 4 liters of lemon-lime soda, 2 pints of sherbet, and 6 cups of ice. How much of e
harkovskaia [24]
Well 18 people is 3/4 of 24 people. So for each ingredient just multiply the value by 0.75.

3 litres of lemon line Soda
1.5 pints of sherbet
4.5 cups of ice
5 0
3 years ago
Other questions:
  • laurie is training for a race. she runs on a path that you s 1.45 miles long. she ran this path 6 times. how many miles did she
    8·1 answer
  • The figure is the net for a rectangular prism. What is the surface area of the rectangular prism represented by the net? PLEASE
    14·1 answer
  • Which number sentence is true? A.|-8| &lt; 8 B.|-15| &lt; 15 C.|-8| &lt; |-15|
    8·1 answer
  • I'm just confused on how to start this first of all and then get the right answer
    7·1 answer
  • Pls help <br> I give 20 points if u help
    12·1 answer
  • Jessie has some nickels, dimes, and quarters in her bank. The number of coins is 30. The expression 0.05n + 0.10d + 0.25q repres
    8·1 answer
  • The expression describe the number that is 8 to the left of -8 on the number line ​
    11·1 answer
  • Find the new price for the markup given. Round to the nearest cent if necessary.
    7·1 answer
  • Students were asked to choose their favorite sport, and 7/9 chose either
    5·1 answer
  • Which fraction below represents a repeating decimal?
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!