Equations and Factoring
The Zero Product Theorems
We have a similar theorem for polynomials:
Example Solve (x - 4) (x + 3) = 0
We have either x - 4 = 0 or x + 3 = 0 Hence the two solutions to (x - 4)(x + 3) = 0 are x = 4 or x = -3
Exercises Solve the following.
Factoring and the Zero Product Rule If we are given a trinomial = 0 then we first factor then we use the zero product rule.
Example Solve x2 - 3x + 2 = 0 We first factor: (x - 2) (x - 1) = 0 Then we use the zero product rule to get x - 2 = 0 or x - 1 = 0 Hence x = 2 or x = 1 Exercises
Solve the following.
Step by Step Process for Solving Using the Zero Product Method For Solving Quadratics
Example Solve 21 = (x - 9) (x + 11)
Solution
Exercises Solve.
Application If air resistance is neglected, then the distance s in feet that an object falls in t seconds is given by s = 16t2 A bolt falls from a bridge 144 feet high. How long does it take to hit the ground?
We set 144 = 16t2 16t2 - 144 = 0 16(t2 - 9) = 0 16(t + 3)(t - 3) = 0 t = -3 or t = 3 Since a negative value for t is meaningless in the problem, we can conclude that it takes three seconds to hit the ground.
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