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Diano4ka-milaya [45]
2 years ago
5

Factor each completely.one zero has been given

Mathematics
1 answer:
Vikentia [17]2 years ago
7 0

The polynomials in <em>factored</em> form are listed below:

  1. <em>f(x) = (x - 3.043) · (x - 1.521 - i 1.716) · (x - 1.521 + i 1.716)</em>
  2. <em>f(x) = (x - 2.236) · (x - 2) · (x + 2.236) · (x + 4)</em>
  3. <em>f(x) = (x + 3) · (x - 5) · (x - 1)</em>
  4. <em>f(x) = (x - 4) · (x - 3) · (x - 1) · x</em>
<h3>How to factor polynomials</h3>

In this question we must factor polynomials as there are both <em>numerical</em> and <em>analytical</em> methods. Mathematically speaking, factoring polynomials is represented by the following formula:

\sum^{n}_{i = 0} \,c_{i}\cdot x^{i} = \prod^{n}_{i=1}(x-r_{i}), \forall\,x, r_{i}\in \mathbb{C}   (1)

Where:

  • c_{i} - i-th Coefficient
  • r_{i} - i-th Root

Regarding <em>fourth order</em> polynomials we can solve them by Ferrari's method and <em>third order</em> polynomials by Descartes' method. Then, the solutions of each polynomials are given below:

<h3>Polynomial 1 (f(x) = x^{3}-4\cdot x +16)</h3>

<em>f(x) = (x - 4) · (x - 3) · (x - 1) · x</em>

<h3>Polynomial 2 (f(x) = x^{4}+2\cdot x^{3}-13\cdot x^{2}-10\cdot x + 40)</h3>

<em>f(x) = (x - 2.236) · (x - 2) · (x + 2.236) · (x + 4)</em>

<h3>Polynomial 3 (f(x) = x^{3}-3\cdot x^{2}-13\cdot x +15)</h3>

<em>f(x) = (x + 3) · (x - 5) · (x - 1)</em>

<h3>Polynomial 4 (f(x) = x^{4}-8\cdot x^{3}+19\cdot x^{2}-12\cdot x)</h3>

<em>f(x) = (x - 4) · (x - 3) · (x - 1) · x</em>

To learn more on polynomials, we kindly invite to check this verified question: brainly.com/question/17822016

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Answer:

40

Step-by-step explanation:

12 + 28

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2 years ago
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a coin must have diameter of 27.13 millimeters.To the nearest hundredth, what is the circumference of this coin millimeters
Bas_tet [7]
To find the circumference, you will use the formula for finding circumference of a circle.

I used the true value of pi for the calculations.

C = pi x d
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4 0
3 years ago
A pyramid with a slant height 4.6 in whose triangular base measures 8 in on each side.Each altitude of the base measures of 6.9
kvasek [131]

Answer:

82.8 in²

Step-by-step explanation:

The surface area a triangular based pyramid :

Base area + 1/2(perimeter * slant height)

Base = 8 inches ; Slant height = 4.6 inches ; altitude of base measure = 6.9 inches

Base area of triangle :

1/2 * base * height

1/2 * 8 * 6.9

4 * 6.9

Base area = 27.6 in²

The perimeter, P = sum of sides ; (s1 + s2 + s3

P = 8 + 8 + 8 = 24 in

Hence,

Surface area = 27.6 in² + 1/2(24*4.6)

Surface area = 27.6 in² + (12 * 4.6) in²

Surface area = (27.6 + 55.2)

Surface area = 82.8 in²

6 0
3 years ago
2(8r+5)-3=4(4r-1)+11 is it an only solution or a no solution or infinite solution
pogonyaev

Answer:

Infinitely many solutions.

Step-by-step explanation:

Let's begin by carrying out the indicated multiplications, which must be done before any addition or subtraction:

2(8r+5)-3=4(4r-1)+11  becomes  16r + 10 - 3 = 16r - 4 + 11.

Subtracting 16r from both sides, we get 10 - 3 = - 4 + 11, or 7 = 7

This is always true, so we can conclude that this equation has infinitely many solutions.

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2 years ago
2. ART An artist created a statue in the shape of a
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Answer is in the photo. I can't attach it here, but I uploaded it to a file hosting. link below! Good Luck!

tinyurl.com/wpazsebu

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