Question

Divide $2x^3-9x^2+10x$ by $(2x+5)$ and also verify the result.

Answer 1

From the fig. we get,

Quotient $=x^2-7x+\frac{45}{2}$

Remainder$=-\frac{225}{2}$

Verify;-

$2x+5=0$

$x=-\frac{5}{2}$ satisfy the equation,

$=2x^3-9x^2+10x$

$=2{\left(\frac{-5}{2}\right)}^3-9{\left(\frac{-5}{2}\right)}^2+10\left(\frac{-5}{2}\right)$

$=2\left(\frac{-125}{8}\right)-9\left(\frac{25}{4}\right)+10\left(\frac{-5}{2}\right)$

$=\left(\frac{-125}{4}\right)-9\left(\frac{25}{4}\right)+10\left(\frac{-5}{2}\right)$

$=\frac{-125}{4}-\frac{225}{4}-\frac{50}{2}$

$=-\frac{225}{2}$

Therefore, $x=-\frac{5}{2}$ satisfy the equation.