Which method can be used to factor the quadratic expression?

Factoring quadratic expressions can be approached through various methods, and trial and error with the roots is often an effective strategy when the expression is relatively simple. This method involves identifying potential rational roots by testing various factors of the constant term relative to factors of the leading coefficient. If a root is found, it signifies that the quadratic can be factored over the integers.

Using trial and error is particularly useful when working with quadratic equations where the coefficients are small integers, making it easier to guess possible factors that satisfy the equation. For example, for a quadratic of the form ( ax^2 + bx + c ), you can try different values for ( x ) until you find a value that yields zero. Once a root is identified, you can factor the quadratic into the form ( (x - r)(ax + s) ), where ( r ) is the root found through your trials.

Other methods such as completing the square or using the quadratic formula may require additional steps or manipulation, making them less straightforward in specific instances, especially if the expression is easily factored through trial and error. Similarly, factoring by grouping can be inefficient unless there is a clear pairing that simplifies the process. Therefore, in simpler cases, trial and error can be