A.

\((x + 3) and (x - 2)\)

B.

\((x - 3) and (x + 2)\)

C.

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

D.

\((x + 3) and (x + 2)\)

Correct answer is **A**

(x - 5) is a factor of \(x^3 - 4x^2 - 11x + 30\). To find the remaining factors, let's draw out \((x - 5)\) from the parent expression.

\(x^3 - 4x^2 - 11x + 30 = x^3 - 5x^2 + x^2 - 5x - 6x + 30\)

\(= x^2(x - 5) + x(x - 5) - 6(x - 5) = (x - 5)(x^2 + x - 6)\)

∴ To find the remaining factors, we factorize \((x2 + x - 6)\)

\(x^2 + x - 6 = x^2 + 3x - 2x - 6\)

\(= x(x + 3) - 2(x + 3) = (x + 3)(x - 2)\)

∴ The other two factors are \((x + 3) and (x - 2)\)

ALTERNATIVELY

\(∴ x^2 + x - 6 = (x + 3) and (x - 2)\)