What is the complete factorization of the polynomial function over the set of complex numbers? f(x)=x3−5x2+4x−20 enter your answer in the box.

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

Step-by-step explanation:

Given that

f(x)=x3−5x2+4x−20

Grouping first two terms together and second set together we have

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

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

These are the factors without complex numbers of f(x)

Equate each factor  to 0 to get

x-5 =0 or x^2+4=0

x =5 or x = square root of -4

i.e. x=5 or x = 2i or x =-2i (since square root of negative number is imaginary)

Factorisation is

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

use formula for the circle a=3.14

step-by-step explanation:

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet