QQuestionMathematics
QuestionMathematics
Which of the following best describes the zero product property?
A. If two factors multiplied together are equal to zero, then at least one of the factors must be zero.
B. If the product of two factors is equal to zero, then both factors must be equal to zero.
C. The product of zero and another factor is always zero.
D. If two nonzero factors are multiplied together, then the product must also be nonzero.
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Answer
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Step 1:I'll solve this step by step with precise LaTeX formatting:
Step 2:: Understand the Zero Product Property
The zero product property is a fundamental algebraic principle that describes the relationship between factors and their product when zero is involved.
Step 3:: Analyze the Given Options
A. $$\text{If } (a \times b = 0) \implies (a = 0 \text{ or } b = 0)
Let's carefully examine each option: This statement is CORRECT. It means that if the product of two factors is zero, then at least one of those factors must be zero. B. This option incorrectly states that BOTH factors must be zero, which is not true. C. This is a true statement about multiplication by zero, but it's not the complete zero product property. D. This statement is incorrect and does not describe the zero product property.
Step 4:: Verify the Reasoning
\text{If } ab = 0, \text{ then } a = 0 \text{ or } b = 0
The zero product property can be mathematically expressed as: This means that if the product of two factors is zero, at least one of those factors must be zero.
Final Answer
Key Insights: - The zero product property is crucial in solving algebraic equations - It helps determine when factors can be zero - It does not require BOTH factors to be zero, just at least one
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