Question

Hello
Please solve the problem

Answer 1

Answer:

g (x) = x² - x + 1

Step-by-step explanation:

We know that,

Dividend = Divisor * Quotient + Remainder    ..... (i)

Here,

Dividend = x³ - 3x² + x + 2

Divisor = g (x)

Quotient = ( x - 2 )

Remainder = ( - 2x + 4 )

Putting the values in (i),

x³ - 3x² + x + 2 = g (x) * ( x - 2 ) + ( - 2x + 4 )

x³ - 3x² + x + 2 + 2x - 4 =  g (x) * ( x - 2 )

x³ - 3x² + 3x - 2 = g (x) * ( x - 2 )

g (x) = $\frac{x^3 - 3x^2 + 3x - 2 }{x -2}$

$\begin{array}{r|lll} & \multicolumn{3}{c}{x^2-x+1}\\ \cline{1-4} x-2 & x^3 & -3x^2&+3x -2 \\ & x^3 & -2x^2 \\ \cline{2-4} && -x^2&+3x -2 \\ && -x^2&+2x \\ \cline{2-4} &&& +x-2\\ &&& +x-2\\ \cline{2-4} &&& \qquad 0 \end{array}$

Therefore, g (x) = Quotient = x² - x + 1

Answer 2

answer is correct or not guys