Answer:
Explanation:
Solving by factoring is a strategy used to find the solutions or roots of a quadratic equation in the form of ax^2 + bx + c = 0. The goal of factoring is to rewrite the equation in the form of (x-r)(x-s) = 0, where r and s are the solutions or roots of the equation. Once the equation is in this form, we can use the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero.
Here is an example to illustrate the process:
Example: Solve the equation x^2 + 5x - 14 = 0 using factoring.
Step 1: Rewrite the equation in standard form (ax^2 + bx + c = 0). In this case, a = 1, b = 5, and c = -14.
Step 2: Factor the equation by looking for two numbers that multiply to give c and add to give b. In this case, the two numbers are -7 and 2, since (-7)(2) = -14 and -7 + 2 = -5.
Step 3: Rewrite the equation as (x + 7)(x - 2) = 0.
Step 4: Use the zero product property to set each factor equal to zero and solve for x.
x + 7 = 0 or x - 2 = 0
x = -7 or x = 2
So the solutions or roots of the equation are x = -7 and x = 2.
It's important to note that not all quadratic equations can be factored, and in such cases, other methods like completing the square or using the quadratic formula should be used.
It's also important to understand that when factoring, it's important to make sure that you have correctly factored the equation, if not the solution will be wrong.