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Grace [21]
3 years ago
8

What is the complete factorization of the polynomial function over the set of complex numbers?

Mathematics
2 answers:
quester [9]3 years ago
6 0

Answer:

f(x)=(x-2)(x+2)(x-5)

Step-by-step explanation:

f(x)=x³-5x²+4x-20                 1. Just group randomly

f(x)=x²(x-5)+4(x-5)                2. Factor the groupings

f(x)=(x²+4)(x-5)                      

<u>f(x)=(x-2)(x+2)(x-5)</u>                3. Factor the difference of two squares

kenny6666 [7]3 years ago
5 0

Answer:(x-5)(x+2i)(x-2i)  is the required factorization of f(x).


Step-by-step explanation:

To factor the expression we must first group the terms and then take out common from these groups

f(x)=x^3-5x^2+4x-20=(x^3-5x^2)+(4x-20)

Taking x^2 common from first group and the 4 from second group we get:


f(x) = x^2(x-5)+4(x-5) = (x-5)(x^2+4)


Now, to factor in complex from we have to break term x^2+4


f(x)= (x-5){x^2-(-2i)^2}

As, i^2 = -1 , therefore (-2i)^2 = 4i^2 =-4

Also using identity a^2-b^2 =(a+b)(a-b)

On solving

f(x) = (x-5)(x+2i)(x-2i)

(x+5)(x+2i)(x-2i)  is the required factorization of f(x).

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<span>12 383 miles => coastline of the United States
      x = Coastline of Canada which is 113,211 miles longer than the coastline of the United States

=>  12 383 miles + 113 211 miles
=>  125 594 miles

Therefore, the coastline of Canada is 125 594 miles which is 113 211 miles longer than the coastline of the United States.

Let’s check if our answer is correct:
=> 125 594 miles – 12 383 miles
=> 113 211 miles (Canada’s coastline is longer than US coastline.)</span>



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