Which of the following is a factor of x3−5x2−2x+24

To find the other factor of the polynomial \( x^3 - 5x^2 - 2x + 24 \) given that \( x - 3 \) is a factor, we can use polynomial long division or synthetic division.

Since \( x - 3 \) is a factor, we can perform synthetic division with the root \( x = 3 \):

1. Write the coefficients of the polynomial: \( 1, -5, -2, 24 \).
2. Set up synthetic division:

\[ \begin{array}{r|rrrr} 3 & 1 & -5 & -2 & 24 \ & & 3 & -6 & -24 \ \hline & 1 & -2 & -8 & 0 \ \end{array} \]

The result of synthetic division gives us the polynomial \( x^2 - 2x - 8 \).

Now we can factor \( x^2 - 2x - 8 \):

\[ x^2 - 2x - 8 = (x - 4)(x + 2) \]

Thus, the complete factorization of \( x^3 - 5x^2 - 2x + 24 \) is:

\[ (x - 3)(x - 4)(x + 2) \]

From the options provided, \( x + 2 \) is indeed a factor.

So the answer is:

x + 2 (x plus 2)