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Reviewing Zero Product Property

8.5.1 Reviewing Zero Product Property

8.5.1 • Reviewing Zero Product Property

Warm Up

Decide whether each statement is true or false.

1.

3 is the only solution to x 2 − 9 = 0 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.

2.

A solution to x 2 + 25 = 0 x 2 + 25 = 0 is –5.

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

3.

x ( x − 7 ) = 0 x ( x − 7 ) = 0 has two solutions.

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

4.

5 and –7 are the solutions to ( x − 5 ) ( x + 7 ) = 12 ( 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 ) ( x − 5 ) ( x + 7 ) at those two values, the result will be 0, not 12.