Question

Dado o polinômio P(x) = -x³ - x² + 1, determinar P (x + 3).

Answer 1

$p(x) = - x {}^{3} - x {}^{2} + 1$

$p(x + 3) = - (x + 3) {}^{3} - (x + 3) {}^{2} + 1$

$p(x+ 3) = - (x {}^{3} + 3x {}^{2} \: . \: 3 + 3x \: . \: 3 {}^{2} + 3 {}^{3} )- (x {}^{2} + 2x \: . \: 3 + 3 {}^{2} ) + 1$

$p(x + 3) = - (x {}^{3} + 9x {}^{2} + 27x + 27) - (x {}^{2} + 6x + 9) + 1$

$p(x + 3) = - x {}^{3} - 9x {}^{2} - 27x - 27 - x {}^{2} - 6x - 9 + 1$

$\boxed{\boxed{\boxed{p(x + 3) = - x {}^{3} - 10x {}^{2} - 33x - 35}}}$

att. yrz