Question
Factor the polynomial: x2−5x+6
Answers
GPT-4o mini
To factor the polynomial \( x^2 - 5x + 6 \), we need to find two numbers that multiply to the constant term (6) and add up to the coefficient of the linear term (-5).
The numbers that satisfy these conditions are -2 and -3, since:
\[
-2 \cdot -3 = 6 \quad \text{(product)}
\]
\[
-2 + (-3) = -5 \quad \text{(sum)}
\]
Thus, we can factor the polynomial as:
\[
x^2 - 5x + 6 = (x - 2)(x - 3)
\]
So, the factored form of the polynomial is \( (x - 2)(x - 3) \).
The numbers that satisfy these conditions are -2 and -3, since:
\[
-2 \cdot -3 = 6 \quad \text{(product)}
\]
\[
-2 + (-3) = -5 \quad \text{(sum)}
\]
Thus, we can factor the polynomial as:
\[
x^2 - 5x + 6 = (x - 2)(x - 3)
\]
So, the factored form of the polynomial is \( (x - 2)(x - 3) \).