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Solving Polynomial Equations – Factoring Method

• A special property is needed to solve polynomial equations by the method of factoring.

If a ∙ b = 0 then a = 0 or b = 0.

Principle of Zero Products

In words, if the product of two quantities is zero, then at least one of the factors must be zero.

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Factoring Method to Solve Polynomial Equations

1. Move all non-zero terms to one side of the equation and simplify.

2. Factor the polynomial expression.

3. Set each factor containing a variable equal to zero.

4. Solve the resulting equations.

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• Example 1:

Move all terms to left side

Factor

Set each factor to zero

Solve each equation.

Solve the equation 2 5x x2 5 0x x ( 5) 0x x

0 5 0x x

0,5x

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• Example 2:

Move all terms to right side since the leading term is positive on that side

Factor

Set each factor to zero

Solve each equation.

Solve the equation 23 24x x 20 3 24x x

0 3 ( 8)x x

3 0 8 0x x

8,0x

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