A rectangular garden has an area represented by the quadratic expression . If the length and width of the garden are both integers, the dimensions are and .
Answer & Analysis
Analysis
Question Analysis
This question tests the student's ability to factor a quadratic expression and apply it to a real-world context. The quadratic expression given is . The goal is to factor this expression into two binomials and then interpret the factors as the dimensions of a rectangular garden.
Key Concept Explanation
Factoring a quadratic expression involves finding two numbers that multiply to the constant term (77) and add up to the coefficient of the linear term (-18). These numbers are -7 and -11, which can be used to factor the quadratic expression.
Step-by-step Solution
1. Identify the factors of 77 that add up to -18: -7 and -11.
2. Rewrite the quadratic expression as:
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