enee 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 x−2 x minus 2 x2+5x+6

Answer 1

To find a factor of the polynomial \( x^3 - 5x^2 + 6x \), we can start by factoring it.

First, we can factor out the common term \( x \):

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

Next, we need to factor the quadratic \( x^2 - 5x + 6 \). We are looking for two numbers that multiply to \( 6 \) and add up to \( -5 \). The numbers \( -2 \) and \( -3 \) fit this requirement.

Thus, we can factor the quadratic:

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

Putting it all together, we have:

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

From this factorization, we see the linear factors are \( x \), \( x - 2 \), and \( x - 3 \).

If \( x \) itself is one of the factors, then another correct factor from the options provided is \( x - 2 \).

Thus, the correct answer is \( x - 2 \).