Question

determinati polinomul P(x) astfel ca 2P(x)=xP(x)-2(x^3-5x^2+8x-4)

Answer 1

$2p(x) = xp(x) - 2( {x}^{3} - 5 {x}^{2} + 8x - 4)$
$2p(x) - xp(x) = - 2( {x}^{3} - 5 {x}^{2} + 8x - 4$
$(x - 2)p(x) = 2( {x}^{3} - 5 {x}^{2} + 8x - 4)$
$p(x) = \frac{ 2{x}^{3} - 10 {x}^{2} + 16x - 8 }{x - 2}$