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+3
x plus 3

x+2
x plus 2

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

x−2

Answer 1

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

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

Next, we need to factor the quadratic polynomial \( x^2 - 5x + 6 \). We can look for two numbers that multiply to 6 (the constant term) and add to -5 (the coefficient of x). These two numbers are -2 and -3.

Therefore, we can factor \( x^2 - 5x + 6 \) as:

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

Putting it all together, we have:

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

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

From the options provided, we can conclude that **\( x - 2 \)** is another correct factor of the polynomial.