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Dominik [7]
2 years ago
12

Find the polynomial function in standard form that has the zeros listed. 1(multiplicity 2), -2(multiplicity 3)​

Mathematics
1 answer:
finlep [7]2 years ago
5 0

Answer:

  f(x) = x⁵ +4x⁴ +x³ -10x² -4x+8

Step-by-step explanation:

If p is a zero, then (x -p) is a factor. The multiplicity of the zero tells you how many times that is a factor (its exponent).

  f(x) = (x -1)²(x +2)³ = (x² -2x +1)(x³ +6x² +12x +8)

  f(x) = x⁵ +4x⁴ +x³ -10x² -4x+8

_____

<em>Additional comment</em>

You can use the distributive property to write out the 12 terms of the product of the two expanded factors, or you can do a little mental arithmetic based on what you know about the exponent of a product term. (It is the sum of the exponents of its factors.)

The mental exercise can be made easier by writing the coefficients of the factors as though they were two cubics. It works well to write them in two rows:

  \left[\begin{array}{cccc}0&1&-2&1\\1&6&12&8\end{array}\right]

The columns are in order of decreasing powers of x. A relatively simple and symmetrical pattern of sums of cross products is used to find the coefficients of the final polynomial. Working in order of decreasing exponents, we have ...

coefficient of x^6 = (0)(1) = 0

coefficient of x^5 = (0)(6) +(1)(1) = 1

coefficient of x^4 = (0)(12) +(1)(-2) +(1)(6) = 4

coefficient of x^3 = (0)(8) +(1)(1) +(1)(12) +(6)(-2) = 1

coefficient of x^2 = (1)(8) +(6)(1) +(-2)(12) = -10

coefficient of x^1 = (-2)(8) +(12)(1) = -4

coefficient of x^0 = (1)(8) = 8

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How many are 1 raised to 3 ???​
Fofino [41]

Answer:

1

Step-by-step explanation:

1^3

This is 1 multiplied by itself 3 times

1*1*1

1

8 0
3 years ago
1. Assume you buy 100 shares of stock at a price of $63.75 per share and incur brokerage fees of $200. You own the stock for 5 y
sdas [7]
1. Your cash flow is as follows.
  initial outlay: $63.75*100 +200.00 = $6575
  quarterly dividend: $0.50*100 = $50 . . . for 19 quarters
  income from sale: $48.63*100 -200.00 +50.00 = $4713
A suitable financial calculator computes the IRR as -3.23% per year.


2. Your cash flow is as follows.
  initial income/outlay: 0
  monthly income: $2750 . . . for 48 months
  monthly income: $3000 . . . for 36 months
  applicable interest rate: .09/12 = 0.0075 . . . per month
A suitable financial calculator computes the NPV as $176,415.70.

3 0
3 years ago
Use the Distributive Property to expand the expression. <br><br>0.4(35m - 15n)​
Alenkasestr [34]
=0.4*35 - 0.4*15
=14-6
=8
boom
4 0
3 years ago
Convert 6 (whole number) 8/11 to a decimal 
Vladimir79 [104]

Answer:

6.73

Step-by-step explanation:

6 (whole number) 8/11 is 6.7272 approximately 6.73 (3 s.f)

the 6 whole number gives the 6.

8/11 is 0 and using the whole long division method gives 0.7272...

cause when you add zero to 8 it becomes 80 and 11 goes into 80, 7 times giving 77.

subtracting 77 from 80 gives 3 adding 0 becomes 30 and 11 into 30 is 2 giving 22

I hope this helps

5 0
2 years ago
What is the solution to this equation?
Komok [63]

Answer:

B. x=75

Step-by-step explanation:

First, write out the equation as you have it:

x/5=15

Then, multiply both sides of the equation by 5/1:

5/1(x/5)=15(5/1)

Your result is:

x=75

5 0
3 years ago
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