Renee is asked to find a factor of x3−5x2+6x , given that x is one of the linear factors. Which of the following is another correct factor?(1 point) Responses x+3 x plus 3 x2+5x+6 x squared plus 5 x plus 6 x−2 x minus 2 x+2

To find a factor of the polynomial \( x^3 - 5x^2 + 6x \), we can first factor out the common term \( x \):

\[
x^3 - 5x^2 + 6x = x(x^2 - 5x + 6)
\]

Now, we need to factor the quadratic \( x^2 - 5x + 6 \). We are looking for two numbers that multiply to \( 6 \) and add to \( -5 \). These numbers are \( -2 \) and \( -3 \), so we can factor the quadratic as follows:

\[
x^2 - 5x + 6 = (x - 2)(x - 3)
\]

Therefore, the complete factorization of the original polynomial is:

\[
x^3 - 5x^2 + 6x = x(x - 2)(x - 3)
\]

Now we know the factors are \( x \), \( x - 2 \), and \( x - 3 \). Given these factors, the question asks for another correct factor.

If \( x \) is one of the linear factors, then from the options provided, the other possible linear factors are:

- \( x - 2 \)
- \( x - 3 \)

The response options provided were:

1. \( x + 3 \)
2. \( x^2 + 5x + 6 \)
3. \( x - 2 \)
4. \( x + 2 \)

Among these options, the only correct factor of \( x^3 - 5x^2 + 6x \) that corresponds with our analysis is:

**\( x - 2 \)**.