factor the trinomial 11

Question

Find the perfect square trinomial whose first two terms are
x squared − 1/2x
? , and then factor the trinomial.

Answer 1

x² - x/2 + c

c = [(1/2)(1/2)]²          completion of square

c = (1/4)²

 

x² - x/2 + (1/4)²

(x - 1/4)²

Answer 2

Jessica,

 

The general rule for completing the square on a binomial

 

x² + bx

 

is to take b, divide it by 2, then square the result.

 

For your problem, b is -1/2. After dividing by 2, you have -1/4. Then squaring, you have (-1/4)² = 1/16.

 

Adding this to what you were given, you will get

 

x² - ½x + 1/16.

 

To factor this, remember that the 1/16 is a square and it came from -1/4. Thus,

 

x² - ½x + 1/16 = (x - ¼)².

 

Let me know if you have any questions.