Chapter 7.1, Problem 16OE

To determine

To Find:

What must be added to make the expression a trinomial square:

  $y^2-3y+?$

Answer to Problem 16OE

  $\frac{9}{4}$

Explanation of Solution

Given:

The expression is :

  $y^2-3y+?$

Calculation:

Given:

  $y^2-3y+?$

First , make the coefficient of $y^2$ 1.

Since here , it already is 1.

Check for the coefficient of y .

It is 3 .

So, the term that has to be added to make it a trinomial and a perfect square is :

square of the half of the coefficient of y

  $={\left(\frac{3}{2}\right)}^2=\frac{9}{4}$

So, $\frac{9}{4}$ should be added.

Check:

  $y^2-3y+\frac{9}{4}={\left(y-\frac{3}{2}\right)}^2$