Q

# On dividing x raised to 3 minus 3x ^ 2 + x + 2 by a polynomial g(x), the quotient and remainder were x- 2 and - 2x + 4, respectively. Find g(x).

Q4   On dividing$x^3 - 3x^2 + x + 2$ by a polynomial g(x), the quotient and remainder were x – 2
and –2x + 4, respectively. Find g(x).

Views

Quotient = x-2

remainder =-2x+4

$\\dividend=divisor\timesquotient+remainder\\x^3-3x^2+x+2=g(x)(x-2)+(-2x+4)\\x^3-3x^2+x+2-(-2x+4)=g(x)(x-2)\\x^3-3x^2+3x-2=g(x)(x-2)\\$

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

Carrying out the polynomial division as follows

$g(x)={x^2-x+1}$

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