Answer:
Solving by Factoring is a strategy used to solve quadratic equations. This strategy involves factoring the quadratic equation. Factoring is breaking an expression down into smaller expressions that when multiplied together will equal the original expression.
Explanation:
To solve a quadratic equation by factoring we must first get the equation into the form ax^2 + bx + c = 0. From here we must use a strategy of factoring known as Reverse FOIL. By using reverse FOIL we will break the equation down into smaller parts. The four steps to use in reverse FOIL are:
1. Find two factors of “ac” (the coefficient of x^2) that when added together equal “b” (the coefficient of x).
2. Multiply the two factors you found in step one to produce “ac.”
3. Group the two terms with the “ac” terms in the equation.
4. Factor the two terms with “bx” in them.
For example, if we have an equation such as 9x^2 + 15x + 4 = 0 we would look for two factors of 4 (ac) that when added together equal 15 (b). The two factors of 4 that when added together equal 15 are -1 and -4. Therefore our equation would become: (9x^2 -1x -4x +4) and we can group the terms like this: (9x^2 -1x)(-4x +4).
The fourth step is to factor the two terms with “bx” in them. In our equation, the two terms with “bx” in them are -1x and -4x. Factoring these terms give us: (9x^2 -1x)(-4x +4) = (3x -1)(3x -4).
The final step is to find the two solutions, or the “x” values, that make the equation equal zero. To find these two x values, just set each factor to zero, and solve the resulting equations. In this example, setting the first factor, (3x - 1) equal to zero, we get x = (1/3); setting the second factor, (3x - 4) equal to zero, we get x = (4/3).
Therefore, the two solutions to 9x^2 + 15x + 4 = 0 are x = (1/3) and x = (4/3).
Using the strategy of Factoring, we have been able to successfully solve the equation 9x^2 + 15x + 4 = 0.