Using the Factor Theorem, the polynomials are given as follows:
1. 
2. 
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 
is given by:
In which a is the leading coefficient.
Item a:
The parameters are:
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
Item b:
The roots are:
Hence:
P(x) = a(x - 4)²x(x + 4)
P(x) = a(x² - 16)x(x - 4)
P(x) = a(x³ - 16x)(x - 4)
It passes through the point x = 5, P(x) = 36, hence:
45a = 36.
a = 4/5
a = 0.8
Hence:
Item 3:
The roots are:
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
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Answer:
1)7.288 feet
2)11.6 feet
3)safe
4) 3.7 feet
5) ∅
6)∅1
∅2
Step-by-step explanation:
1) The door barn is rectangular in shape. The length is 9 feet and The angle between diagonal and side is 39 degrees.
Applying trigonometry,
tan(39) = 
= 0.809
Thus, s= 
2) Applying pythagoras theorm,
Diagonal length (d) = 11.58 feet. Nearest tenth place = 11.6 feet
3) The length of ladder is 14 foot and height from ground is 13.5 feet.
Applying trigonometry,
sin(∅) = 
= 0.964
∅ = angle of elevation = 
= 74.57 ≈ 75 degrees.
Thus tractor can climb safely.
4)Applying, pythgoras theorm,
x = 
Thus, ladder should be placed at distance 3.7 feet
5)Let angle of elevation be ∅.
tan(∅) = 
∅
6)After moving 5 feet closer to barn, Let angle of elevation for light near barn be ∅1 and for farther one be ∅2.
Thus,
tan(∅1) = 
∅1
tan(∅2) = 
∅2
9514 1404 393
Answer:
Molly
Step-by-step explanation:
Brady did not properly create a square.
The square of a binomial is ...
(a -b)² = a² -2ab +b²
Where a²=x² and -2ab = -4x, you find b=2. The constant term in the square is 2²=4. Brady shows it as -4, which is incorrect.
Molly's work is correct.
Answer:
(-3) - (-6) = -3+6 = 6-3 = 3
Step-by-step explanation:
Lets solve:
- - Solve for that to get answer:
24.3
Your final answer is 24.3
