Question

If $\frac{3}{2}{x}^2-a=3$ has a remainder $-1$ when divided by $x-2$, then what will be the value of $a$?

• A. $4$
• B. $3$
• C. $2$
• D. $1$

Answer 1

The correct option is A $4$

Replace $x$ as $2$ in the expression:
$\frac{3}{2}{x}^2-a=3$

$\frac{3}{2}{2}^2-a=3$

$\frac{3}{2}\times 4-a=3$

$6-a=3$
$=3-a$
So, the remainder is $3-a$, Now substitute the value of remainder, we know it is $-1$.
$3-a=-1$
$3+1=a$
$a=4$