Question

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+2
x plus 2

x2+5x+6
x squared plus 5 x plus 6

x+3
x plus 3

x−2

Answer 1

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

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

Next, we need to factor the quadratic \( x^2 - 5x + 6 \). To do this, we look for two numbers that multiply to 6 and add up to -5. The two numbers that fit this criterion 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:

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

The linear factors of \( x^3 - 5x^2 + 6x \) are \( x \), \( x - 2 \), and \( x - 3 \).

Since the question asks for another correct factor, and \( x \) is already provided as a factor, the correct responses from the options given would be:

- \( x - 2 \)
- \( x - 3 \), if it was listed as an option (which it is not).

Therefore, the correct response from the provided options is:

**x - 2**.