To find a factor of the polynomial \( x^3 - 5x^2 + 6x \), we can start by factoring it.
First, we can factor out the greatest common factor, which is \( x \):
\[ x^3 - 5x^2 + 6x = x(x^2 - 5x + 6) \]
Next, we need to factor the quadratic \( x^2 - 5x + 6 \). We are looking for two numbers that multiply to \( 6 \) (the constant term) and add up to \( -5 \) (the coefficient of \( x \)). The numbers that meet these criteria are \( -2 \) and \( -3 \). Thus, we can factor the quadratic as follows:
\[ x^2 - 5x + 6 = (x - 2)(x - 3) \]
Putting it all together, we have:
\[ x^3 - 5x^2 + 6x = x(x - 2)(x - 3) \]
Now that we fully factored the polynomial, we find that the factors of \( x^3 - 5x^2 + 6x \) are \( x \), \( x - 2 \), and \( x - 3 \).
Now, looking at the options provided:
- \( x^2 + 5x + 6 \)
- \( x + 3 \)
- \( x + 2 \)
- \( x - 2 \)
The correct factors that we found are \( x \), \( x - 2 \), and \( x - 3 \). Therefore, \( x - 2 \) is indeed one of the correct factors.
Thus, the answer to the question of which of the listed options is another correct factor is:
\[ \boxed{x - 2} \]
1 answer