Question

divide 3x square-x cube -3x+5 by x-1-x square and verify the division algorithm​

Answer 1

Explanation:

Wehavep(x)=x

3

−3x

2

+5x−3

andg(x)=x

2

−2

Long division method :

x²-2)x³-3x²+5x-3(x-3

***** x³ + 0 -2x

______________

********* -3x²+7x-3

********* -3x²+ 0 +6

________________

Remainder ( 7x-9)

________________

Dividend p(x) = x³-3x²+5x-3,

Divisor g(x)= x²-2 ,

Quotient q(x)= x - 3 ,

Remainder r(x) = 7x - 9

\underline { \blue { Division \: Algorithm }}

DivisionAlgorithm

\boxed {\pink { Dividend = divisor \times quotient + Remainder }}

Dividend=divisor×quotient+Remainder

g(x) \times q(x) + r(x)g(x)×q(x)+r(x)

= (x^{2}-2)(x-3)+(7x-9)=(x

2

−2)(x−3)+(7x−9)

\begin{lgathered}= x^{2}(x-3)-2(x-3)+7x-9 \\= x^{3}-3x^{2}-2x+6+7x-9 \\= x^{3}-3x^{2}+5x-3\\= Dividened\end{lgathered}

=x

2

(x−3)−2(x−3)+7x−9

=x

3

−3x

2

−2x+6+7x−9

=x

3

−3x

2

+5x−3

=Dividened