Question

What is the remainder of (2x3 − 18x + 5) ÷ (x − 3)?

Answer 1

the remainder is five. heres the proof.

Answer 2

Answer: The required remainder is 5.

Step-by-step explanation: We are given to find the remainder of the following division :

`(2x^3-18x+5)/ (x-3).`

We have the following theorem :

FACTOR THEOREM : If f(x) is a polynomial, then the remainder on dividing f(x) by (x - a) is f(a).

For the given division, we have

`f(x)=2x^3-18x+5,\\\\(x-a)=(x-3)~~~~~\Rightarrow a=3.`

Therefore, the remainder when f(x) is divided by (x - 3) is given by

`f(3)=2*3^3-18*3+5=54-54+5=5.`

Thus, the required remainder is 5.