91Ó°ÊÓ

Factoring a quadratic equation involves expressing it as the product of two binomials. This is useful when you are looking to solve the equation for its roots. Let's break down the process:

1. **Identify Coefficients**: Start by identifying the coefficients of the quadratic equation in the form: y^2 + by + c = 0 y^2 + 12y + 4 = 0where a = 1 (the coefficient of y^2), b = 12, and c = 4.

2. **Find Factor Pairs**: Next, we need to find two numbers that multiply together to get `c` (4 in this case) and add up to `b` (12 in this instance).y^2 + 12y + 4 = (y + a)(y + b)We factor out y^2 + 12y + 4 = (y + 6)(y + 6)Notice how (y + 6)(y + 6) expands back to y^2 + 12y + 36Identifying these numbers can sometimes be tricky, which is when other methods like completing the square can become handy.

The method of completing the square involves modifying a quadratic equation so that one side of the equation becomes a perfect square trinomial. Here's how you can do it step-by-step:

1. **Rewrite the Quadratic**: Move the constant term to the other side of the equation, if necessary.y^2 + 12y + 4 = y^2 + 12y = -4

2. **Form a Perfect Square**: Modify the equation to form a perfect square trinomial on one side.y^2 + 12y + 36 = (y + 6)^2You can get