Simplify: 26u3 + 273
2 answers:
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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:
Step-by-step explanation:
Given that special deck of cards has 20 cards. Nine are green, seven are blue, and four are red. When a card is picked, the color of it is recorded. An experiment consists of first picking a card and then tossing a coin
A) Sample space will have Green, Head, or Green, Tail .... Red, head, red, tail
No of elements in sample space = no of colours x no of outcomes in coin toss
= 4x2 = 8
B) A= getting (RT)
P(A) = Prob of getting red card and tail on coin
= P (R) *P(T)
=
C) B be the event that a green or blue is picked, followed by landing a tail on the coin toss
B = getting green card and tail
Getting green card tail is mutally exclusive with red card and tail as there is no common element between green and blue.
D) C= red or green card is picked followed by tail.
Here A and C have a common element as getting red and tail. So not mutually exclusive