Respuesta :
Answer:
see explanation
Step-by-step explanation:
Given
n² - 23n - 24 = 0
To factor the quadratic
Consider the factors of the constant term (- 24) which sum to give the coefficient of the n- term (- 23)
The factors are - 24 and + 1, since
- 24 × 1 = - 24 and - 24 + 1 = - 23, thus
(n - 24)(n + 1) = 0 ← in factored form
Given a polynomial with degree 2
[tex]ax^2+bx+c[/tex]
we can factor it as long as it has solutions. If we have
[tex]ax^2+bx+c=0 \iff x=x_1 \lor x=x_2[/tex]
then we have
[tex]ax^2+bx+c=a(x-x_1)(x-x_2)[/tex]
In this case, the solutions are given by two numbers that give -24 when multiplied, and 23 when summed. These numbers are clearly 24 and -1.
So, given the roots [tex]x_1=-1,\ x_2=24[/tex], the factorization would be
[tex]n^2-23n-24=(x+1)(x-24)[/tex]
