Zero Factor Property is not a Property of Quadratic Equations

Share Cognitive Science Implications for Teaching Mathematics
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The Zero Factor Property is a property of the Real Numbers and should be taught as such.  We do our students a great disservice when we lead them astray into believing that The Zero Factor Property is simply a technique for solving certain quadratic equations.  To teach The Zero Factor Property properly as a property of The Real Numbers requires conscious effort o0n the part of teachers.  It should be presented and used long before quadratic equations are introduced.  A few examples of how this might be done are:

Example 1: Solve equations like (3x + 2)x = 0 during a discussion of solving linear equations in one variable.

Example 2: Solve equations like (2x + 7)(9x – 4)(x + 3) = 0 during a discussion of linear equations in one variable.

Example 3: During a discussion of linear equations in one variable, use the Distributive Property and The Zero Factor Property to solve equations like x(2x + 5) + 7(2x + 5) = 0.

Example 4:  During a discussion of linear equations in one variable use the Distributive Property and The Zero Factor Property to solve equations like 3x3(x – 8) = 0.

Example 5: During a discussion of linear equations in one variable find some solutions of equations like (7x – 8)(7x3 + 5x – 11)= 0.

Example 6: During a discussion of linear equations in one variable solve equations like      (4x + 8)(9x + 1) = 0.

Example 7: Solve equations like (x4 + 5)(x3 – 8) = 0

Example 8: When discussing factoring, long before introduction of the exponential or logarithm functions, you should teach students how to factor expressions like e2x – 2ex -15. During that discussion, point out that consideration of an equation like e2x – 2ex -15 = 0 is equivalent to the equation (ex – 5)(ex + 3) = 0 and the Zero Factor Property informs us that is equivalent to the two equations ex – 5 = 0 or ex + 3 = 0. So although we might not know (at this point in time) how to solve exponential equations we know what will be required to solve that original equation.

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