Factoring Polynomials

Ron is studying vertical motion in physics class. He wants to find the time it takes for a ball thrown straight upward at twenty meters per second to return to his hand.

Using the vertical motion equations, he sets the initial height to zero and substitutes 20 for the initial velocity and negative 10 for the acceleration due to gravity.

When the ball returns to the release point, its height is zero. He substitutes these values into the equation and gets a quadratic equation.

Before solving, he looks for a factor shared by both terms. The coefficients 20 and 5 are both divisible by 5, and both terms also contain t.

So, the greatest common monomial factor is 5t. Factoring out 5t gives 5t times the quantity t minus 4 equals zero. For this product to equal zero, at least one factor must be zero.

Setting each factor equal to zero gives t = 0 and t = 4. Since t = 0 is the instant when the ball is released, Ron concludes that the ball returns to the release point after 4 seconds.