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mel-nik [20]
3 years ago
14

(X-2) is a factor of x^4+2x^3-7x^

Mathematics
1 answer:
zysi [14]3 years ago
6 0

Answer:

x−2x4+2x3−7x2−8x+12=x3+4x2+x−6

The rational root theorem suggests that other possible roots may be -6, 6, -3, 3, -2, 2, -1, and 1. It turns out that x=-2x=−2 is a root, since (-2)^3+4(-2)^2+(-2)-6=0(−2)3+4(−2)2+(−2)−6=0 , so x+2x+2 is also a factor and we have

\dfrac{x^4+2x^3-7x^2-8x+12}{(x-2)(x+2)}=x^2+2x-3(x−2)(x+2)x4+2x3−7x2−8x+12=x2+2x−3

Finally, we can factorize the remaining quotient easily:

x^2+2x-3=(x+3)(x-1)x2+2x−3=(x+3)(x−1)

so the other factors are x+2x+2 , x+3x+3 , and x-1x−1 .

You might be interested in
How do you solve 39 equal to 1 3/10b
elena-s [515]
If 39 = (1 3/10)b, we could simplify this by writing 39 - (13/10)b.

Solve this for b by mult. both terms by (10/13):

(10*39)
----------- = (10/13)(13/10)b.  Then b = 30 (answer)
      13
5 0
3 years ago
What is the value of f?
laiz [17]

Answer:

f(1/2) = -2

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

<u>Algebra I</u>

  • Function Notation

Step-by-step explanation:

<u>Step 1: Define</u>

f(x) = 8x - 6

f(1/2) is x = 1/2

<u>Step 2: Evaluate</u>

  1. Substitute in <em>x</em>:                    f(1/2) = 8(1/2) - 6
  2. Multiply:                               f(1/2) = 4 - 6
  3. Subtract:                              f(1/2) = -2
5 0
3 years ago
The sum of the arithmetic progression 4, ..., 76 is 1920. Find the number of terms and the common difference.​
valkas [14]

<u>Number of terms = 48</u>

<u>common difference = 1.5</u>

This question involves the concept of Arithmetic Progression.

  • The formula for sum of an arithmetic progression series with first and last term given is;

S_{n} = \frac{n}{2}(a + l)

where;

a = first term

l = last term

n = number of terms

  • From the given sequence, we see that;

first term; a = 4

last term; l = 76

Sum of A.P; S_{n} = 1920

  • Plugging in relevant values into the sum of an AP formula, we have;

1920 = \frac{n}{2}(4 + 76)

simplifying this gives;

1920 = 40n

n = 1920/40

n = 48

  • Formula for nth term of an AP is;

t_{n} = a_{1} + (n - 1)d

where;

a_{1} is first term

d is common difference

n is number of term

t_{n} is the nth term in question

the 48th term is 76

Thus;

76 = 4 + (48 - 1)d

76 - 4 = 47d

72 = 47d

d = 72/47

d ≈ 1.5

Thus;

Number of terms = 48

common difference = 1.5

Read more at; brainly.com/question/16935540

4 0
3 years ago
Пожалуйста,очень нужны 4,5,6<br> Срочнооооооо<br> Спасибо заранее
kifflom [539]
B. is the answer to your question!! Hope this helps!! :D
4 0
3 years ago
The sum of three consecutive even integers is -114.
Alika [10]
The sum of three consecutives is b 
5 0
3 years ago
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