Question

answer it correctly plzz​

Answer 1

Answer:

answer for the given problem is given

Answer 2

Here,

It is given that

$\rm : \bullet \: \:polynomial \: p(x) = {x}^{3} - {3x}^{2} + x + 2$

$\rm : \bullet \: quotient \: q(x) \: = x - 2$

$\rm : \bullet \: remainder \: r(x) = - 2x + 4$

Now,

We have to find the divisor g(x).

We know,

Using Divison Algorithm,

• Dividend = Divisor × Quotient + Remainder

$\boxed{ \green{ \rm : \implies \:f(x) \: = \: g(x) \times q(x) + r(x) }}$

On substituting the values, we get

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

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

$\rm : \implies \:g(x) \times (x - 2) = {x}^{3} - {3x}^{2} + 3x - 2$

$\rm : \implies \:g(x) = \dfrac{{x}^{3} - {3x}^{2} +3 x - 2}{(x - 2)}$

On dividing by long division, see the attachment, we get

$\rm : \implies \:g(x) = {x}^{2} - x + 1$