Question

what is the remainder when you divide \\((2x^3 - 5x - 7)\\) by \\((x + 2)\\)? -9 -13 3 19

Explanation:

Step1: Apply Remainder Theorem

For polynomial $f(x)$ divided by $(x-a)$, remainder is $f(a)$. Here, $x+2=x-(-2)$, so $a=-2$.

Step2: Define the polynomial

Let $f(x)=2x^3 -5x -7$

Step3: Substitute $x=-2$ into $f(x)$

$$\begin{align*} f(-2)&=2(-2)^3 -5(-2) -7\\ &=2(-8) +10 -7\\ &=-16 +10 -7 \end{align*}$$

Step4: Calculate the result

$$ -16 +10 -7 = -13 $$

Answer:

-13