Question
Solve the following quadratic
function by factoring.
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:
-
Identify two numbers that multiply to 28 and add up to 11:
- The numbers are 4 and 7 because:
- The numbers are 4 and 7 because:
-
Factor the quadratic equation using these numbers:
-
Set each factor equal to zero and solve for
: -
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: