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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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UL
Kay [80]

Answer:

<em>4(y+2) = 3(x+4) and 4y - 3x = 4</em>

Step-by-step explanation:

The equation of the line in point slope form is expressed as;

y - y0 = m(x-x0)

m is the slope

(x0, y0) is the point on the line

Given the equation 3x - 4y = 7

Rewrite in slope intercept form

-4y = -3x+7

y = 3/4 x - 7/4

Slope = 3/4

Slope of the required line will also be 3/4  since they are parallel lines

Substitute the slope and the point into the equation above;

y - y0 = m(x-x0)

y +2 = 3/4 (x+4)

4(y+2) = 3(x+4)

4y + 8 = 3x+12

4y - 3x = 12-8

4y - 3x = 4

<em>Hence the required equations are 4(y+2) = 3(x+4) and 4y - 3x = 4</em>

3 0
3 years ago
Mr . Jackson sold 3 computer monitors in the 1st year. In the 2nd year, he sold 4 times as many monitors as the 1st year. In the
tester [92]
So,

1st year: 3
2nd year: 4(first year), which is 12
3rd year: 6(first year), which is 18

The sum of the 1st, 2nd, and 3rd years is 3 + 12 + 18 = 33

Now, multiply 33 by the price at which Mr. Jackson sold each computer ($185).

We get $6105.  Mr. Jackson's gross profit was $6105.


3 0
2 years ago
The answers ......................... to number 4 and the bonus
Flauer [41]
.............................

7 0
2 years ago
Match the graph with its function by translating the graph of y=\sqrt()x
Makovka662 [10]

Answer:?

Step-by-step explanation:

4 0
3 years ago
21r-7-r+5=-52 solve for r
malfutka [58]

Answer:

r = - 2.5

r=-2\frac{1}{2}

Step-by-step explanation:

21r - 7 - r + 5 = - 52

20r - 2 = - 52

20r - 2 + 2 = - 52 + 2

20r = - 50

20r ÷ 20 = - 50 ÷ 20

r = - 2.5

3 0
2 years ago
Read 2 more answers
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