Explanation:
Factoring using the quadratic form involves using the quadratic formula to find the two values that, when multiplied together, give the original quadratic equation. The quadratic formula is as follows:
x = (-b ± √(b^2 - 4ac)) / 2a
To use the quadratic formula to factor a quadratic equation, first rewrite the equation in the form of ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable. Then, plug the values of a, b, and c into the quadratic formula to solve for x. The two values of x that you find are the factors of the original quadratic equation.
Here's an example:
Suppose you want to factor the quadratic equation 2x^2 + 7x + 3 = 0. In this case, a is 2, b is 7, and c is 3. Plugging these values into the quadratic formula, we get:
x = (-7 ± √(7^2 - 4 * 2 * 3)) / 2 * 2
Solving this equation, we get x = (-7 ± √(49 - 24)) / 4, which simplifies to x = (-7 ± √(25)) / 4. Since the square root of 25 is 5, we can further simplify this to x = (-7 ± 5) / 4, which gives us the solutions x = -1 and x = -3/2.
Therefore, the two factors of the original equation 2x^2 + 7x + 3 = 0 are x + 1 and x + 3/2.