constant trinomial 9.1 12

Question

Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial.
 
x squared + 1/2x

 

What is the constant that should be added to the binomial so that it becomes a perfect square? trinomial?

Answer 1

The constant is half of the coefficient of the x term, squared.  The x term is (1/2)x, so the coefficient is 1/2.  Take 1/2 of it: (1/2)*(1/2) = 1/4.  Now square it: (1/4)² = 1/16.  So 1/16 is the constant you need to add.

 

x² +(1/2)x + 1/16

 

Factors to:

 

(x + 1/4) ²

Answer 2

When the coefficient of x squared is one, then the magic number that you must add to create a perfect square trinomial is one half of the coefficient of x (power 1 term). In this case, ½•½=¼ is the desired number.