Question

solve using long division method: 3x³-5x²-11x-3 by (x-3) and verify it also using this formula : D=d×Q+R ​

Answer 1

Answer:

Step-by-step explanation:

3x³-5x²-11x-3

=. 3x²(x-3)+4x(x-3)+1(x-3)

= (x-3) (3x²+4x+1)

if devide x-3 then result will be (3x²+4x+1)

Answer 2

$\large\underline{\sf{Solution-}}$

Given that,

$\rm :\longmapsto\:Dividend = {3x}^{3} - {5x}^{2} - 11x - 3$

$\rm :\longmapsto\:Divisor = x - 3$

So, Using Long Division, we have

$\red{\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{}}}&{\underline{\sf{\:\: 3{x}^{2} + 4x + 1\:\:}}}\\ {\underline{\sf{x - 3}}}& {\sf{\: 3{x}^{3}  -  {5x}^{2} - 11x - 3 \:\:}} \\{\sf{}}& \underline{\sf{\:\:   - 3 {x}^{3} + 9{x}^{2}  \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:   \:\:}} \\ {{\sf{}}}& {\sf{\: \:  \: 4{x}^{2} - 11x - 3  \:  \:\:}} \\{\sf{}}& \underline{\sf{\:\: - 4{x}^{2} + 12x  \:  \:  \:  \:  \:  \: \:\:}} \\ {\underline{\sf{}}}& {\sf{\:\: \:  \:  \: \: \: x - 3  \:\:}} \\{\sf{}}& \underline{\sf{\: \:  \:  \: \: - x + 3\:\: \: \: }} \\ {\underline{\sf{}}}& {\sf{\:\: \:    \:  0\:\:}}  \end{array}\end{gathered}\end{gathered}\end{gathered}}$

Hence,

We get

$\rm :\longmapsto\:Quotient = {3x}^{2} + 4x + 1$

and

$\rm :\longmapsto\:Remainder = 0$

Now, we have

$\rm :\longmapsto\:Dividend = {3x}^{3} - {5x}^{2} - 11x - 3$

$\rm :\longmapsto\:Divisor = x - 3$

$\rm :\longmapsto\:Quotient = {3x}^{2} + 4x + 1$

$\rm :\longmapsto\:Remainder = 0$

Now, Consider,

$\rm :\longmapsto\:Divisor \times Quotient + Remainder$

$\rm \: = \:(x - 3)( {3x}^{2} + 4x + 1)$

$\rm \: = \:{3x}^{3} + 4 {x}^{2} + x - {9x}^{2} - 12x - 3$

$\rm \: = \: {3x}^{3} - {5x}^{2} - 11x - 3$

$\rm \: = \:Dividend$

Hence, Verified