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Dovator [93]
2 years ago
15

Only questions 5 and 6 pls.

Mathematics
1 answer:
lesantik [10]2 years ago
4 0

theres no pic so how do we answer

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MAT 171
steposvetlana [31]

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

5 0
2 years ago
When 415415 junior college students were​ surveyed, 125125 said that they have previously owned a motorcycle. find a point estim
Bingel [31]
About 125,000/415,000 junior college students
I think you forgot the decimal points

4 0
3 years ago
Write a real word problem that can be solved using the equation 5x=3x+20
igor_vitrenko [27]
Andy and Diana both got some pocket money from their aunt.

Andy spent all his money on collector's coins, he bought 5 of them.

Diana bought 3 of such coins, and she brought home 20 dollars of change.

after they came home their sister said "hah! I bet you I can find out how much each coin costs even if you don't tell me how much money your aunt gave you, if she gave  you both the same amount!"

So, how much does each coin cost?
8 0
3 years ago
The function C(x) = 17.5.0 - 10 represents the cost (in dollars) of buying a tickets to the orchestra with a $10 coupon a How mu
aliina [53]

Answer:

8

Step-by-step explanation:

8 0
3 years ago
please help. The floor area of a square closet is 16 ft2. What is the length of one side of the closet?
Greeley [361]

Answer:

4 feet

Step-by-step explanation:

A square has 4 sides.

16/4=4 feet

Hope this helps =]

3 0
3 years ago
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