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abruzzese [7]
3 years ago
8

Determine all the factors for the following expression(Note: you will need to use the Rational Root Theorem more than one time)

: f(x)=x^5+3x^4-5x^3-15x^2+4x+12? Please help im so confused and this assignment is due tomorrow!?

Mathematics
2 answers:
Aleks [24]3 years ago
4 0
ANSWER

Possible rational roots: <span><span>±1,±2,±3,±4,±6,±12</span><span>±1,±2,±3,±4,±6,±12</span></span>

Actual rational roots: <span><span>1,−1,2,−2,−3</span></span>

<span><span>see attachments for all steps.</span></span>

____ [38]3 years ago
4 0
Possible roots are formed using the last term (12) of the given function and the 1st term (1) as your basis:

Since factors of 12 include plus or minus 1, 2, 3, 4, 6, 12,

possible rational roots include plus or minus 1/1, 2/1, 3/1, 4/1, 6,/1, 12/1 (and so on.)   I will take a chance and try the possible root 6/1, or just plain 6.

Use synthetic division, with 6 as the divisor and all of the coefficients of    <span>x^5+3x^4-5x^3-15x^2+4x+12   as dividend:
       ______________________
  6  /  1   3   -5   -15   4    12
               6  54
       --------------------------------
          1   9   49   This is not going to work; 6 is not a root.  

Try -3 as divisor:


        ___________________
</span>  -3  /  1   3   -5   -15   4    12
               -3    0     15  0   -12
       -------------------------- ------
          1    0   -5      0   4     0

Since the remainder is zero, x = -3 is a root of the given polynomial.  

Repeat this process, except skip x = -3 and x = 6 as divisors.

Use the coefficients    1   0   -5   0   4.  Note that plus or minus 4 over 1 forms other possible rational roots:  4/1, -4/1, 2/1, -2/1, 1, -1

Let's check out          
    ____________
1 /  1  0  -5  0   4
           1  1  -4    -4
--------------------------
      1   1  -4  -4    0
Thus, 1 is also a root of the polynomial, along with -3.

Repeat this process.  As divisors try 4/1, -4/1, 2/1, -2/1, -1

Can you now finish this factoring?

The 2 roots found so far are {1, -3}.
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If the length of each side of a cuboid decreases by 20%, find the percentage decrease in its volume.
just olya [345]

Answer:

Step-by-step explanation:

(1+25 /100) (1-20/100) (1-50/100)  <1

5/4 x 4/5 x 1/2 <1

Decrease in volume (in percent)

(1+25 /100) (1-20/100) (1-50/100)  x 100

=48.8%

6 0
2 years ago
Somebody please help me
WITCHER [35]

Step-by-step explanation:

x - 1 = - 3x - 14

Bringing like terms on one side

x + 3x = -14 + 1

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5 0
2 years ago
In 2010 an item costs $9.00. The price increases by 1.5% each year. How much will it be in 2030?
Yanka [14]

Answer:11.7

Step-by-step explanation:

1. Recognize variables. Starting price is 9, it’s increasing by 1.5% each year, the question asks for the price in 20 years.

2. Convert percentage to decimal. Most calculators won’t understand multiplying by percentages, and instead will understand multiplying by decimals. A decimal is something we can easily work with. It is more commonly taught to work with decimals as well. With that said 1.5% equals .015. (The number in the ones place in the percentage is always in the hundredths place when converted to a decimal, the tens to the tenths, the hundreds in the percentage to the ones place in the decimal, the hundredths in the percentage to the ten thousandths in the decimal. Basically, every individual number [the 5 in 1.5] moves two spaces to the right when going from percentage to decimal form, likewise two to the left going from decimal to percentage form. 23%=.23, 104%=1.04, 0.5%=.05, 1.234%=.01234)

3. Make your equation

20(9*(.015))+9

+9 is your starting point

9*(.015) gives you the amount the price increases per year

20 is multiplied then to that increased price for the next 20 years

4. Crunch em numbers

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5 0
3 years ago
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mart [117]

x adds 1 and y subtracts by 6

7 0
3 years ago
Twenty words were randomly selected from two textbooks. Each set gives the number of letters in each of the twenty words for tha
Alborosie

Answer:

k = 13The smallest zero or root is x = -10

Step-by-step explanation:

you can write "x^2" to mean "x squared"

f(x) = x^2+3x-10

f(x+5) = (x+5)^2+3(x+5)-10 ... replace every x with x+5

f(x+5) = (x^2+10x+25)+3(x+5)-10

f(x+5) = x^2+10x+25+3x+15-10

f(x+5) = x^2+13x+30

Compare this with x^2+kx+30 and we see that k = 13

Factor and solve the equation below

x^2+13x+30 = 0

(x+10)(x+3) = 0

x+10 = 0 or x+3 = 0

x = -10 or x = -3

The smallest zero is x = -10 as its the left-most value on a number line.

7 0
3 years ago
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