Question

if $p(x) = 2x^3 - 7x^2 - 3x - 25$, what is the remainder of $p(x) \div (x + 3)$?

1. $-133$
2. $-43$
3. $0$
4. $35$

Explanation:

Step1: Apply Remainder Theorem

For polynomial $p(x)$ divided by $(x-a)$, remainder is $p(a)$. Here, $x+3=x-(-3)$, so $a=-3$.

Step2: Substitute $x=-3$ into $p(x)$

$$p(-3)=2(-3)^3 -7(-3)^2 -3(-3) -25$$

Step3: Calculate each term

$2(-3)^3=2(-27)=-54$; $-7(-3)^2=-7(9)=-63$; $-3(-3)=9$; constant term $=-25$

Step4: Sum all terms

$$p(-3)=-54 -63 +9 -25$$
$$p(-3)=(-54-63-25)+9$$
$$p(-3)=-142+9=-133$$

Answer:

1. -133