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mart [117]
3 years ago
9

Factor the polynomial function over the complex numbers. f(x)=x^4-x^3-2x−4 Enter your answer in the box. f(x) = The answer is: (

x−2)(x+1)(x+i2√)(x−i2√)
Mathematics
1 answer:
Vladimir79 [104]3 years ago
8 0

Answer:

Factors: (x+i\sqrt2)(x-i\sqrt2)(x+1)(x-2)=0

Step-by-step explanation:

We are given a polynomial:

f(x)=x^4-x^3-2x-4

We have to factor the given polynomial into its complex factors.

The factorization can be done as follows:

f(x)=x^4-x^3-2x-4 = 0\\x^4-x^3-2x-4 = 0\\x^4-4-x^3-2x=0\\\text{Identity: }a^2-b^2 = (a+b)(a-b)\\(x^4-4)-(x^3+2x) = 0\\(x^2+2)(x^2-2)-x(x^2+2) = 0\\(x^2+2)(x^2-2-x) = 0\\(x^2+2)(x^2-x-2) = 0\\(x^2+2)(x^2-2x-+x-2) = 0\\(x^2+2)((x(x-2)+1(x-2))=0\\(x^2+2)(x+1)(x-2)=0\\\text{Identity: }a^2-b^2 = (a+b)(a-b)\\(x^2-(\sqrt{-2})^2)(x+1)(x-2)=0\\(x+i\sqrt2)(x-i\sqrt2)(x+1)(x-2)=0

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2x+4=12 helppppppppppppppp​
Anni [7]

Answer:

x=4

Step-by-step explanation:

1. 2x+4=12

2. 2x+4-4=12-4

3. 2x=8

4. 2x/2=8/2

5. x=4

3 0
2 years ago
Read 2 more answers
A student council consists of 15 students. Two council members have the same major and are not permitted to serve together on a
tiny-mole [99]

Answer: 4004ways

Step-by-step explanation:

Total number of Students =15

Total number of students to be on the committee =5

Since two members are of the same major and must not be on the committee, then we are left with choosing 5 people from just 14 People after we eventually remove one from those two students with same majors.

Hence to select 5 people from 14 people, we use the combination formula 14C5.

From the two students with same major we also use the combination Formula in knowing the number of ways any of the two students can be chosen. To choose one from these two students, we use the combination Formula 2C1.

Hence, the total number of ways to choose the committee of 5 and ensuring the two students with same major aren't on the committee becomes:

= 14C5 * 2C1

= 2002 * 2

= 4004ways.

3 0
3 years ago
How many extraneous solutions does the equation below have?
FrozenT [24]

<u>Answer</u>

0


<u>Explanation</u>

(2m)/(2m+3)-(2m)/(2m-3)=1

Simplifying the left hand first

(2m)/(2m+3)-(2m)/(2m-3) = {2m(2m-3) - 2m(2m+3)}/(4m²-9)

                                        (4m²-6m-4m²-6m)/(4m²-9)

                                         = (-12m) / (4m²-9)

Now this equet to 1

(-12m) / (4m²-9) = 1

-12m =  4m²-9

4m²+ 12m -9 =0 ⇒⇒⇒ This is a quadratic equation that has 2 real solutions.

4m²+ 12m -9 =0

m² + 3m + (3/2)²= 9/4 + 9/4

(m + 3/2)² = 18/4

m = √18/2 - 3/2                or m = -√18/2 - 3/2

    = 0.621                                       = -3.621

So we can say that the equation has NO extraneous solutions.

Answer = 0

8 0
3 years ago
Read 2 more answers
12 chocolate bars for $22 or 20 chocolate bars for $33 use unit rate to determine the better buy.
jekas [21]
12c=22
6c=11
c=1 5/6
20c=33
c= 1 13/20
5/6 is about .83
13/20 is .65
12 chocolate bars for $22 is about $1.83 each
20 chocolate bars for $33 is $1.65 each

The 20 chocolate bars for $33 dollars has a better unit rate and is a better buy.
6 0
3 years ago
Which of the following rules describes the pattern in the table?
sattari [20]

Answer:

b = e + 4

b = e + 4 i think that is the pattern in the table

6 0
3 years ago
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