Question

Use the Remainder Theorem to find the remainder: (–6x3 + 3x2 – 4) ÷ (2x – 3).

Answer 1

We have that
(–6x³ + 3x² – 4) ÷ (2x – 3)
----------------------║--------------------------
   +6x³+9x²              -3x²+6x+9
---------------------
12x²-4
-------------------
-12x²+18x
-------------------
18x-4
-----------------
-18x+27
----------------
23-----------------> the remainder

the answer is 23

Answer 2

Answer:  The correct option is (B) -17.5.

Step-by-step explanation:  We are given to use the Remainder Theorem to find the remainder for the following division :

$(-6x^3+3x^2-4)\div(2x-3)$

Remainder Theorem :  When a polynomial p(x) is divided by the linear factor (x - a), then the remainder is equal to p(a).

We have

$2x-3=0\\\\\Rightarrow 2x=3\\\\\Rightarrow x=\dfrac{3}{2}$

So, the remainder for the given division is given by

$R\\\\=-6\times\left(\dfrac{3}{2}\right)^3+3\times\left(\dfrac{3}{2}\right)^2-4\\\\\\=-6\times\dfrac{27}{8}+3\times\dfrac{9}{4}-4\\\\\\=-\dfrac{81}{4}+\dfrac{27}{4}-4\\\\\\=\dfrac{-81+27-16}{4}\\\\\\=-\dfrac{70}{4}\\\\=-17.5$

Thus, the required remainder is -17.5.

Option (B) is CORRECT.