Question
Divide each of the following polynomials by synthetic division method and also by linear division method. Write the quotient and the remainder : $(2m^2 – 3m + 10) ÷ (m – 5)$
✓
Answer
Synthetic division:
$\left(2 m^2-3 m+10\right) \div(m-5)$
Dividend $=2 m^2-3 m+10$
$\therefore$ Coefficient form of dividend $=(2,-3,10)$
Divisor $=m-5$
$\therefore$ Opposite of $-5$ is $5$ .
Coefficient form of quotient $=(2,7)$
$\therefore$ Quotient $=2 m+7$,
Remainder $=45$
Linear division method:
$2 m^2-3 m+10$
To get the term $2 m^2$, multiply $(m-5)$ by $2 m$ and add $10 m$,
$=2 m(m-5)+10 m-3 m+10$
$=2 m(m-5)+7 m+10$
To get the term 7 m , multiply $(m-5)$ by $7$ and add $35$
$=2 m(m-5)+7(m-5)+35+10$
$=(m-5)(2 m+7)+45$
$\therefore \text { Quotient }=2 m+7$
$\text { Remainder }=45$
$\left(2 m^2-3 m+10\right) \div(m-5)$
Dividend $=2 m^2-3 m+10$
$\therefore$ Coefficient form of dividend $=(2,-3,10)$
Divisor $=m-5$
$\therefore$ Opposite of $-5$ is $5$ .
Coefficient form of quotient $=(2,7)$
$\therefore$ Quotient $=2 m+7$,
Remainder $=45$
Linear division method:
$2 m^2-3 m+10$
To get the term $2 m^2$, multiply $(m-5)$ by $2 m$ and add $10 m$,
$=2 m(m-5)+10 m-3 m+10$
$=2 m(m-5)+7 m+10$
To get the term 7 m , multiply $(m-5)$ by $7$ and add $35$
$=2 m(m-5)+7(m-5)+35+10$
$=(m-5)(2 m+7)+45$
$\therefore \text { Quotient }=2 m+7$
$\text { Remainder }=45$
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