Question

Encontre ovalor numérico da expressão polinomial p(x) = (x-2)³ + 4x - 5 
Encontre o valor numérico da expressão polinomial p(x) = (x-2)³ + 4x - 5 
a) X =0
b) x= 2/3

Answer 1

$p(x)=(x-2)^3+4x-5\\ \\ a) \ p(0)=(0-2)^3+4.0-5=-8-5=-13\\ \\ b) \ p(\frac{2}{3})=(\frac{2}{3}-2)^3+4*\frac{2}{3}-5=-\frac{127}{27}$

Answer 2

$P(x)=(x-2)^3+4x-5$

a) $x=0$

$P(0)=(0-2)^3+4(0)-5$

$P(0)=(-2)^3+0-5~~\Rightarro~~P(0)=-8-5~~\Rightarrow~~\boxed{P(0)=-13}$

b) $x=\dfrac{2}{3}$

$P\left(\dfrac{2}{3}\right)=\left(\dfrac{2}{3}-2\right)^3+4\cdot\dfrac{2}{3}-5$

$P\left(\dfrac{2}{3}\right)=\left(-\dfrac{4}{3}\right)^3+\dfrac{8}{3}-5$

$P\left(\dfrac{2}{3}\right)=-\dfrac{64}{27}+\dfrac{8}{3}-5$

$P\left(\dfrac{2}{3}\right)=\dfrac{-64+72-135}{27}~~\Rightarrow~~\boxed{P\left(\dfrac{2}{3}\right)=-\dfrac{127}{27}}$