Question

when (9x⁴ - 45x³ + 37x² + x + 2) is divided by (x - 2), find the remainder. 652 -368 -64 656

Explanation:

Step1: Apply Remainder Theorem

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

Step2: Define the polynomial

$f(x)=9x^4 - 45x^3 + 37x^2 + x + 2$

Step3: Calculate $f(2)$

$$\begin{align*} f(2)&=9(2)^4 - 45(2)^3 + 37(2)^2 + 2 + 2\\ &=9(16) - 45(8) + 37(4) + 4\\ &=144 - 360 + 148 + 4\\ &=-64 \end{align*}$$

Answer:

-64