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: To answer your question: If two of the angles of two triangles are the same, the triangles are similar. ... If two of the angles are known, the third can be found by subtracting the two known angles from 180. If the three angles of two triangles are the same, the triangles have the same shape and are similar.
Step-by-step explanation:: I have now explained to you why the Angle- Angle Triangle Similarity Theorem works i hope Iwas able to help good luck
Answer:
5/12
Step-by-step explanation:
First, list the months by the number of days each has:
Jan: 31, Feb: 28 or 29, Mar: 31, Apr: 30, May: 31, Jun: 30, Jul: 31, Aug: 31, Sep: 30, Oct: 31, Nov: 30, Dec: 31.
How many of these 12 months have an even number of days?
Feb, Apr, Jun, Sep, Nov (assuming that we ignore Leap Year): 5 months
Then the probability that the selected month will have an even number of days is
5 months
--------------- = 5/12
12 months
Furstly, multiplying mixed fractions together is chaotic. Convert them into improper fractions first.
(22/3) * (20/3) * (27/10)
Secondly, don't start multiplying all out! Look for common factors. There are two 3's at the denominator, and 27 is 3^3 at the numerator. Cross them out!
22 * 20 * 3 / 10
Hey! There are multiples of 10 too!
22 * 2 * 3
= (11 * 2) * 2 * 3
= 11 * 12
= 132
That leads to option 3!
