perfect square trinomial to square of a binomial

Question

x^211x+ 

 

x^2 -15x+

 

s^2- 2/3s +

 

h^2-3/4h+ 

Answer 1

For each of these, you'll need to add some constant that makes the trinomial a perfect square.

 

Here's an example:

 

x² + 6x + ____

 

Add half of the middle term (6) squared:

 

x² + 6x + (6/2)²

x² + 6x + 3²

x² + 6x + 9

(x+3)(x+3)

(x+3)²

 

FOIL that back out to see why it needs to be half the middle term squared. We want the constant for the binomial (3) to be half the middle term of the trinomial, since we'll get 3x + 3x = 2(3)x = 6x. And we want the constant for the binomial to be that value (3) squared, since we'll get (3)(3) = 3².

 

 

 

I'll pick one of yours to work out as another example:

 

s² - 2/3s + ____

 

Half of -2/3 is (1/2)(-2/3) = -2/6 = -1/3.

-1/3 squared is (-1/3)(-1/3) = 1/9.

 

s² - 2/3s + 1/9

(s - 1/3)(s - 1/3)

(s - 1/3)²

 

 

 

Try the rest on your own.