Question
Divide first polynomial by second polynomial and write the answer in the form 'Dividend = Divisor x Quotient + Remainder':
$5 x^5+4 x^4-3 x^3+2 x^2+2 ; x^2-x$
$5 x^5+4 x^4-3 x^3+2 x^2+2 ; x^2-x$
✓
Answer
$5 x^5+4 x^4-3 x^3+2 x^2+2=5 x^5+4 x^4-3 x^3+2 x+0 x+2$
$\therefore$ Quotient $=5 x^3+9 x^2+6 x+8$,
Remainder $=8 x +2$
Now, Dividend = Divisor $x$ Quotient + Remainder
$\therefore 5 x^5+4 x^4-3 x^3+2 x^2+2=\left(x^2-x\right)\left(5 x^3+9 x^2+6 x+8\right)+(8 x+2)$
$\therefore$ Quotient $=5 x^3+9 x^2+6 x+8$,
Remainder $=8 x +2$
Now, Dividend = Divisor $x$ Quotient + Remainder
$\therefore 5 x^5+4 x^4-3 x^3+2 x^2+2=\left(x^2-x\right)\left(5 x^3+9 x^2+6 x+8\right)+(8 x+2)$
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