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7nadin3 [17]
3 years ago
6

Divide the following polynomials using synthetic division, then place the answer in the proper location on the grid. Write answe

r in descending powers of x. (x3 - 2x2 - 1) ( x - 1)
Mathematics
1 answer:
insens350 [35]3 years ago
3 0
To solve using synthetic division:

Draw an upside down division symbol (I did the best I can given the format). Place the constant of x - 1 (1) on the outside, and the coefficients of x³ - 2x² - 1 on the inside, like so:      

   | x³   x²   x¹   x⁰
1 | 1   -2    0   -1   
   |         
   |___________

Next, bring down the first coefficient.

    | x³   x²   x¹   x⁰
  1| 1   -2    0   -1   
    |         
    |___________ 
      1

Multiply the number on the outside of the symbol (1) by the coefficient you've just brought down (1). Place that number under the next coefficient to the right.

    | x³   x²   x¹   x⁰
  1| 1   -2    0   -1    
    |       1   
    |___________ 
      1

Add the new number (1) to the coefficient above it (-2) and place that number directly underneath it.

    | x³   x²   x¹   x⁰
  1| 1   -2    0   -1    
    |       1   
    |___________ 
      1   -1

Continue this process until you've run out of numbers to multiply.

    | x³   x²   x¹   x⁰
  1| 1   -2    0   -1    
    |       1   -1   -1
    |___________ 
      1   -1   -1   -2

The resulting numbers are coefficients. The first three are part of the quotient, and the last one is part of the remainder. The remainder becomes the last coefficient (-2) over the divisor (x - 1).

Answer:
(x³ - 2x² - 1) / (x - 1) = x² - x - 1 + -2/x - 1
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Answer:

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f'(t)=0.001155t(t-1980)^{0.5}

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\int \frac{df(t)}{dt}dt=f(t)=\int [0.001155t(t-1980)^{0.5}]dt

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Then, the function f(t) is:

f(t)=0.001155[\frac{2}{3}t(t-1980)^{3/2}-\frac{4}{15}(t-1980)^{5/2}]+C'

The value of C' is deduced by the information of the exercise. For t=0 there were 264,034,000 outpatient​ visits.

Hence C' = 264,034,000

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b) For t = 2015 you have:

f(t=2015)=0.001155[\frac{2}{3}(2015)(2015-1980)^{1/2}-\frac{4}{15}(2015-1980)^{5/2}]+264,034,000\\\\f(t=2015)=264,034,317.7

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</span>n-a number

n = b - 5

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