Answer:
Factors are (n + 5)(n - 4) = 0 .
Explanation:
Given : The sum of the squares of 2 consecutive negative integers is 41. What are the numbers.
To find : Which of the following equations is the result of using the factoring method to solve the problem.
Solution : We have given statement
Let two consecutive number are : n and n +1 .
Square of two consecutive number are : n² and (n+1)².
According to question : sum of the squares of 2 consecutive negative integers is 41.
n² + (n+1)² = 41.
n² + n² + 1 +2n =41
2n² + 2n +1 =41
On subtracting 41 from both sides
2n² + 2n +1- 41 = 0
2n² + 2n - 40 = 0
On dividing by 2 to whole equation
n² + n - 20 = 0
On factoring
n² + 5n -4n - 20 = 0
Taking common n from first two terms and -4 from first two last terms
n (n +5) -4 (n +5) = 0
Grouping
(n -4) (n +5) = 0.
Therefore, Factors are (n + 5)(n - 4) = 0 .