Question

on dividing x cube - 3 X square + X + 2 by a polynomial g(x), the quotient and remainder were x - 2 and - 2 X + 4 respectively. find g(x) .​

Answer 1

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ゝWE KNOW THE FORMULA,

$✯ \: dividened = divisor \times quotient + remainder$

$✯p(x) = g(x) \times q(x) + r(x)$

$✯substitute \: the \: given \: values$

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

$✯ add \: 2x \: and \: subtract \: 4 \: both \: sides$

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

$✯simplify \: and \: divide \: by \: x - 2$

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

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

$\boxed{✯so \: g(x) = {x}^{2} - x + 1}$

see in attachment also ✌️