8.4.1 Introducing the Zero Product Property

Algebra 18.4.1 Introducing the Zero Product Property

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Warm Up

What values of the variables make each equation true?

Enter the value of a.

$6 + 2 a = 0$

$- 3$

Enter the value of b.

$7 b = 0$

$0$

Enter the value of c.

$7 (c - 5) = 0$

$3$

Determine which of the statements are true if $g \cdot h = 0$ . HINT: There may be more than one statement that is true.

(g=0\), $h = 0$ , and $g = h = 0$ . Either $g = 0$ or $h = 0$ . But also, notice, if $g = 0$ and $h = 0$ at the same time, you can also say that $g = h = 0$ .

What did you notice about one of the factors in each of the previous problems?

Enter what you noticed.

Compare your answer:

At least one of the factors in each equation was 0 or equivalent to 0.

We will use the zero product property to help solve quadratic equations throughout this lesson.

ZERO PRODUCT PROPERTY

If the product of two expressions is 0, then one or both of the expressions equal 0.

If $a b = 0$ , then $a = 0$ or $b = 0$ , or $a = b = 0$ .

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- Authors: Lynn Marecek, MaryAnne Anthony-Smith, Andrea Honeycutt Mathis, Jay Abramson, Sharon North, Amy Baldwin, Alyssa Howell
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- Book title: Algebra 1
- Publication date: Jun 4, 2025
- Location: Houston, Texas
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- Section URL: https://openstax.org/books/algebra-1/pages/8-4-1-introducing-the-zero-product-property

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