Solve for T Leave your answer in simplest radical form.
1 answer:
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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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complete question:
A mini game cube is covered in different colors and has a side length of 1.8 inches. Which of the following would represent the amount of space covered in various colors?
A. 116.64 in2
B. 3.24 in2
C. 19.44 in2
D. 10.8 in2
Answer:
C. 19.44 in2
Step-by-step explanation:
A cube is a 3 dimensional figure bounded by 6 square faces. All the sides of a cube are equal in length. The picture below is a cube. The amount of space covered in different colors will be the surface area of the cube.
surface area = 6L²
where
L = length
L = 1.8 inches
surface area = 6 × 1.8²
surface area = 6 × 3.24
surface area = 19.44 inches²
