Question

Rewrite each expression as a polynomial in standard form(x-(2+i))(x-(2-i))

Answer 1

Answer:

x² - 4 x + 3

Step-by-step explanation:

given expression              

  ( x - ( 2 + i ) )( x - ( 2 - i ) )      

on solving                        

 = x² - (2 - i )x - (2 + i) x  + (2 + i )(2 - i)

 = x² - 2 x + i x - 2 x - i x + 2² - i²

using identity                    

(a+ b)(a-b) = a² - b²                  

 = x² - 4 x + 2 - (-1)                                   ∵ i² = -1

= x² - 4 x + 2 + 1                        

= x² - 4 x + 3                                          

hence, the required polynomial equation is x² - 4 x + 3