Question number 10.

Use synthetic division to evaluate $P(-4)$ for
$$P(x)=x^3-4x^2-9x+36$$
18
21
26
10
16

Step 1 ：Write down the coefficients of the polynomial $P(x)$, which are 1, -4, -9, and 36.

Step 2 ：Write down the value we are evaluating the polynomial at, which is -4.

Step 3 ：Set up the synthetic division as follows: $$-4|1-4-936$$

Step 4 ：Perform the synthetic division: $$-4|1-4-936$$ $$\phantom{-4|}-432-92$$ $$\phantom{-4|}-----------------$$ $$\phantom{-4|}1-823-56$$

Step 5 ：The numbers in the bottom row are the coefficients of the quotient polynomial, and the last number, -56, is the remainder.

Step 6 ：Since we are evaluating $P(-4)$, the remainder is the value of the polynomial at $x=-4$.

Step 7 ：$P(-4)=-56$

Step 8 ：Therefore, none of the options 18, 21, 26, 10, 16 are correct.

Step 9 ：$\boxed{{\displaystyle P(-4)=-56}}$ is the correct answer.