8.5.1 Reviewing Zero Product Property

Algebra 18.5.1 Reviewing Zero Product Property

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Warm Up

Decide whether each statement is true or false.

3 is the only solution to $x^{2} - 9 = 0$ .

False. There are two solutions because there are two numbers that can be squared to get 9. Both 3 and –3 are possible solutions.

A solution to $x^{2} + 25 = 0$ is –5.

False. There is no solution to $x^{2} + 25 = 0$ because no real number can be squared to get –25.

$x (x - 7) = 0$ has two solutions.

True. There are two factors, 0 and 7, that could make the product of the expression 0.

5 and –7 are the solutions to $(x - 5) (x + 7) = 12$ .

False. The product of the two factors is not 0, so we cannot solve it using the zero product property (which gives 5 and –7 as solutions). If we evaluate the expression $(x - 5) (x + 7)$ at those two values, the result will be 0, not 12.

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