Explain the process of factoring a quadratic expression.

Factoring a quadratic expression involves finding two binomials that, when multiplied together, give the original expression.

To factor a quadratic expression, we first look for common factors that can be factored out. For example, in the expression 2x^2 + 6x, we can factor out 2x to get 2x(x + 3).

If there are no common factors, we can use the quadratic formula to find the roots of the expression. The roots will give us the factors of the expression. For example, in the expression x^2 + 5x + 6, the roots are -2 and -3. Therefore, we can factor the expression as (x + 2)(x + 3).

Another method for factoring quadratic expressions is to use the method of completing the square. This involves adding and subtracting a constant term to the expression to create a perfect square trinomial, which can then be factored. For example, to factor the expression x^2 + 6x + 5, we can add and subtract 1 to get x^2 + 6x + 1 - 1 + 5. This can be rewritten as (x + 3)^2 - 1, which factors to (x + 2)(x + 4).

In some cases, factoring a quadratic expression may not be possible using these methods. In such cases, we can use the quadratic formula to find the roots of the expression.