Multiply (x - 4)(x^2 - 5x - 6).

Step-by-step solution

1. 1

   Set up the distribution. FOIL only covers binomial times binomial. With a trinomial you distribute each term of $(x-4)$ across all three terms, giving $2 \times 3 = 6$ products to collect.

2. 2

   Distribute the $x$.

   $x(x^2 - 5x - 6) = x^3 - 5x^2 - 6x$

3. 3

   Distribute the $-4$. Two sign flips happen here, so go slowly: $-4 \times -5x = +20x$ and $-4 \times -6 = +24$.

   $-4(x^2 - 5x - 6) = -4x^2 + 20x + 24$

4. 4

   Add the two rows and collect like terms.

   $x^3 + (-5x^2 - 4x^2) + (-6x + 20x) + 24 = x^3 - 9x^2 + 14x + 24$

5. 5

   Sanity-check the leading and constant terms. The leading term must be $x \cdot x^2 = x^3$ ✓ and the constant must be $(-4)(-6) = +24$ ✓ — a negative constant would have been an immediate sign error. Distractors such as $x^3 - x^2 + 26x + 24$ and $x^3 - 5x^2 + 10x + 24$ get the ends right but the middle wrong.

6. 6

   Verify with a test value. At $x = 2$ the original is $(2-4)(4-10-6) = (-2)(-12) = 24$, and the expansion gives $8 - 36 + 28 + 24 = 24$ ✓.