Ask AI: n²-10n+9 factor

Sure, let's factor the quadratic expression \( n^2 - 10n + 9 \). To factor a quadratic expression of the form \( ax^2 + bx + c \), we look for two numbers that multiply to \( ac \) (in this case, \( 1 \times 9 = 9 \)) and add up to \( b \) (in this case, -10). 1. Identify \( a \), \( b \), and \( c \): - \( a = 1 \) - \( b = -10 \) - \( c = 9 \) 2. We need two numbers that multiply to 9 and add up to -10. These numbers are -1 and -9. 3. Rewrite the middle term (\( -10n \)) using these numbers: \[ n^2 - n - 9n + 9 \] 4. Group the terms: \[ (n^2 - n) + (-9n + 9) \] 5. Factor out the greatest common factor (GCF) from each group: \[ n(n - 1) - 9(n - 1) \] 6. Factor out the common binomial factor \( (n - 1) \): \[ (n - 1)(n - 9) \] So the factored form of \( n^2 - 10n + 9 \) is: \[ (n - 1)(n - 9) \]