Question

If $\frac{2}{3}{x}^2-x+5b$ has a remainder $-1$ when divided by $x+2$, then what will be $b$?

• A. $\frac{-7}{15}$
• B. $\frac{-17}{15}$
• C. $\frac{-1}{15}$
• D. $\frac{17}{15}$

Answer 1

The correct option is B $\frac{-17}{15}$

Replace $x$ as $-2$ in the expression:
$\frac{2}{3}{x}^2-x+5b$
$=$ $\frac{2}{3}(-2{)}^2-(-2)+5b$

$=$ $\frac{2}{3}\times 4+2+5b$

$=$ $\frac{14+15b}{3}$
So, the remainder is $\frac{14+15b}{3}$, now substitute the value of remainder as $-1$.
$\frac{14+15b}{3}$ $=-1$
$14+15b=-3$
$15b=-3-14$
$15b=-17$
$b=$ $\frac{-17}{15}$