Question

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

Answer 1

Answer:  The required remainder is 5.

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

$(2x^3-18x+5)\div (x-3).$

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

$f(3)=2\times3^3-18\times3+5=54-54+5=5.$

Thus, the required remainder is 5.

Answer 2

The remainder is five. heres the proof.