Question
factor the completely n^2-7n+12
Answers
GPT-4o mini
To factor the quadratic expression \( n^2 - 7n + 12 \), we need to find two numbers that multiply to \( 12 \) (the constant term) and add up to \( -7 \) (the coefficient of the linear term).
The numbers that satisfy these conditions are \( -3 \) and \( -4 \):
- \( -3 \times -4 = 12 \)
- \( -3 + -4 = -7 \)
Thus, we can factor the expression as follows:
\[
n^2 - 7n + 12 = (n - 3)(n - 4)
\]
So, the completely factored form is:
\[
(n - 3)(n - 4)
\]
The numbers that satisfy these conditions are \( -3 \) and \( -4 \):
- \( -3 \times -4 = 12 \)
- \( -3 + -4 = -7 \)
Thus, we can factor the expression as follows:
\[
n^2 - 7n + 12 = (n - 3)(n - 4)
\]
So, the completely factored form is:
\[
(n - 3)(n - 4)
\]