Question
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Solve the following quadratic
function by factoring.

Ask by Barrett Franklin. in the United States
Jan 30,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The solutions are and .

Solution

To solve the quadratic equation by factoring, follow these steps:
  1. Identify two numbers that multiply to 28 and add up to 11:
    • The numbers are 4 and 7 because:
  2. Factor the quadratic equation using these numbers:
  3. Set each factor equal to zero and solve for :
  4. Enter the smallest solution first:
Final Answer:

Answered by UpStudy AI and reviewed by a Professional Tutor

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The Deep Dive

To solve the quadratic function by factoring, we need to express it as a product of two binomials. We look for two numbers that multiply to (the constant term) and add up to (the coefficient of the linear term).
The numbers and work because:
Thus, we can factor the quadratic as:
Setting this equal to zero gives us the solutions:
The solutions are and . Therefore, the final answer with the smallest solution first is:

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