Question
factor the common 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 to \( -7 \) (the coefficient of the linear term).
The numbers that satisfy these conditions are \( -3 \) and \( -4 \), since:
- \( -3 \times -4 = 12 \)
- \( -3 + (-4) = -7 \)
Therefore, we can factor the quadratic as follows:
\[
n^2 - 7n + 12 = (n - 3)(n - 4)
\]
So, the factored form of \( n^2 - 7n + 12 \) is \( (n - 3)(n - 4) \).
The numbers that satisfy these conditions are \( -3 \) and \( -4 \), since:
- \( -3 \times -4 = 12 \)
- \( -3 + (-4) = -7 \)
Therefore, we can factor the quadratic as follows:
\[
n^2 - 7n + 12 = (n - 3)(n - 4)
\]
So, the factored form of \( n^2 - 7n + 12 \) is \( (n - 3)(n - 4) \).