Question

what is the remainder r when the polynomial p(x) is divided by (x - 5)?
p(x) = x³ - 5x² + 2x - 10
options: 0, 2x - 10, -2x - 10, 2x + 10

Explanation:

Step1: Apply Remainder Theorem

For polynomial $p(x)$ divided by $(x-a)$, remainder is $p(a)$. Here $a=5$.

Step2: Substitute $x=5$ into $p(x)$

$$p(5) = 5^3 - 5\times5^2 + 2\times5 - 10$$

Step3: Calculate each term

$$5^3=125,\ 5\times5^2=125,\ 2\times5=10$$

Step4: Compute final value

$$p(5)=125 - 125 + 10 - 10 = 0$$

Answer:

0