Question

03)Dado o polinômio P(x) = x3 - 5x2 + x - 1 ,calcule :
a) P(1)
b) P(-1)
c) P(-2)
d) P(1⁄2)
e) P( 3)
f) P(0)

Answer 1

Explicação passo-a-passo:

$03)$

$p(x) = x {}^{3} - 5x {}^{2} + x - 1$

$a)p(1) = 1 {}^{3} - 5.1 {}^{2} + 1 - 1 = 1 - 5 + 1 - 1 = - 4$

$b)p( - 1) = ( - 1) {}^{3} - 5.( - 1) {}^{2} - 1 - 1 = - 1 - 5 - 1 - 1 = - 8$

$c)p( - 2) = ( - 2) {}^{3} - 5.( - 2) {}^{2} - 2 - 1 = - 8 - 10 - 2 - 1 = - 21$

$d)p( \frac{1}{2} ) = ( \frac{1}{2} ) {}^{3} - 5.( \frac{1}{2} ) {}^{2} + \frac{1}{2} - 1 =$

$\frac{1}{8} - 5 \times \frac{1}{4} + \frac{1}{2} - 1 = \frac{1}{8} - \frac{5}{4} + \frac{1}{4} - 1$

m.m.c=8

$\frac{1 + 10 + 4 - 8}{8} = \frac{7}{8}$

$e)p(3) = (3) {}^{3} - 5 \times (3) {}^{2} + 3 - 1 = 27 - 45 + 3 - 1 = - 15 - 1 = - 16$

$f)p(0) = 0 {}^{3} - 5 \times (0) {}^{2} + 0 - 1 = - 1$