Factoring Second Degree Polynomials

One common form of a second-degree polynomial is x squared plus bx plus c. Factoring means rewriting the polynomial as the product of binomial expressions.

To factor this type of trinomial, we use the trial-and-error method. We look for two numbers whose product is the constant term, c, and whose sum is the coefficient of the linear term, b.

This method helps solve real-world problems. For example, while testing an automated emergency braking system, an engineer models a vehicle’s velocity using the expression t squared minus 4t minus 12.

To find when the vehicle comes to a complete stop, he sets the expression equal to zero.

To factor this quadratic expression, he looks for two numbers that multiply to negative twelve and add to negative four. Negative six and positive two work.

So, the expression factors as the product of t plus 2 and t minus 6. Solving the equation gives t equals negative 2 seconds and t equals 6 seconds.

Since time cannot be negative in the real world, t equals negative 2 is excluded. The vehicle comes to a complete stop in exactly 6 seconds.