Remainder theorem is a theorem in algebra: if f(x) is a polynomial in x then the remainder on dividing f(x) by x-a is f(a).

In algebra, the factor theorem is a theorem linking factors and zeros of a polynomial. It is special case of the polynomial remainder theorem.

(v) $2{{x}^{3}}-3{{x}^{2}}+6x-4$is divided by $\left( 2x-3 \right)$

Solution:-

From the question it is given that, $2{{x}^{3}}-3{{x}^{2}}+6x-4$is divided
by $\left( x+4 \right)$

Let us assume $2x-3=0,x={3}/{2}\;$

Now, substitute the value of x in given expression,

$=2{{\left( 3/2 \right)}^{3}}-3{{\left( 3/2 \right)}^{2}}+6\left( 3/2
\right)-4$

$=\left( 2\times 27/8 \right)-3\left( 9/4 \right)=\left( 3\times 3
\right)-4$

$=27/4-27/4+9-4$

$=9-4$

Therefore, the remainder of the given expression $5.$