Find the remainder (without division) on dividing 3x^2 + 5x – 9 b… - Vidyadip

Question

Find the remainder (without division) on dividing $3x^2 + 5x – 9 by (3x + 2)$

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Answer

Let $3 x+2=0$,
then $3 x=-2$
$\Rightarrow x=\frac{-2}{3}$
Substituting the value of $x$ in $f(x)$
$ f(x)=3 x^2+5 x-9$
$=3\left(-\frac{2}{3}\right)^2+5\left(-\frac{2}{3}\right)-9$
$=3 \times \frac{4}{9}-5 \times \frac{2}{3}-9$
$=\frac{4}{3}-\frac{10}{3}-9$
$=-\frac{6}{3}-9$
$=-2-9$
$=-11$
$\therefore \text { Remainder }=-11 .$

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