Complete the square for the binomial. Then factor the resulting perfect square trinomial.

Question

x² +4/7x

Answer 1

Starting binomial: x² + (4/7)x

 

Complete the square with a = 1, b = 4/7, and c = 0:

 

     Take half of b: b/2 = 2/7

 

 

     Square b/2: (b/2)² = (2/7)² = 4/49

 

 

     Add and subtract (b/2)²:  x² + (4/7) x + (2/7)² - (2/7)²

 

 

     1st 3 terms form a square trinomial: [x² + (4/7) x + (2/7)²] - (2/7)²

 

    

     Rewriting the trinomial as a square: (x + 2/7)² - (2/7)²

 

     

     Factor the difference of squares:

 

     [(x + 2/7) + 2/7][(x + 2/7) - 2/7]