Question

if p(x)=2x² - 3x + 5, what is the remainder when p(x) is divided by x - 5? (1) - 230 (2) 0 (3) 40 (4) 240

Explanation:

Step1: Apply Remainder Theorem

According to the Remainder Theorem, if a polynomial $p(x)$ is divided by $x - a$, the remainder is $p(a)$. Here $a = 5$ and $p(x)=2x^{2}-3x + 5$.

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

$p(5)=2\times5^{2}-3\times5 + 5$.
First, calculate $2\times5^{2}=2\times25 = 50$.
Then, $3\times5 = 15$.
So $p(5)=50-15 + 5$.

Step3: Simplify the expression

$p(5)=40$.

Answer:

(3) 40