Final answer:
A quadratic equation in standard form can be converted to factored form by finding two numbers that multiply to a × c and add to b, then expressing the equation as the product of two binomials.
Step-by-step explanation:
The question involves converting a quadratic equation from standard form to factored form. Consider a quadratic equation in standard form: ax² + bx + c = 0. To convert this into factored form, we need to find two numbers that multiply to a × c and add to b. We then use these numbers to write the quadratic as a product of two binomials.
Let's assume a quadratic equation 4.90t² - 14.3t - 20.0 = 0. The constants are a = 4.90, b = -14.3, and c = -20.0. First, identify two numbers that multiply to (4.90 × -20.0) and add to -14.3. Once you find those numbers, you rewrite the equation as (pt + q)(rt + s) = 0, where p, q, r, and s are numbers derived from the identified pair. From here, you can solve the quadratic equation for t using factoring methods.