Resposta:
[tex]\textsf{Leia abaixo}[/tex]
Explicação passo a passo:
[tex]\mathsf{P(x) = [(x - 1).(x - 2).(x - 3)].k}[/tex]
[tex]\mathsf{P(x) = [(x - 1).(x^2 - 3x - 2x + 6)].k}[/tex]
[tex]\mathsf{P(x) = [(x - 1).(x^2 - 5x + 6)].k}[/tex]
[tex]\mathsf{P(x) = [x^3 - 5x^2 + 6x - x^2 + 5x - 6].k}[/tex]
[tex]\mathsf{P(x) = [x^3 - 6x^2 + 11x - 6].k}[/tex]
[tex]\mathsf{P(0) = [(0)^3 - 6.(0)^2 + 11(0) - 6].k}[/tex]
[tex]\mathsf{P(0) = [0 - 0 + 0 - 6].k}[/tex]
[tex]\mathsf{P(0) = -6k}[/tex]
[tex]\mathsf{1 = -6k}[/tex]
[tex]\mathsf{k = -\dfrac{1}{6}}[/tex]
[tex]\mathsf{P(10) = [(10)^3 - 6(10)^2 + 11(10) - 6].\left(-\dfrac{1}{6}\right)}[/tex]
[tex]\mathsf{P(10) = [1000 - 600 + 110 - 6].\left(-\dfrac{1}{6}\right)}[/tex]
[tex]\mathsf{P(10) = \left(-\dfrac{504}{6}\right)}[/tex]
[tex]\boxed{\boxed{\mathsf{P(10) = -84}}}[/tex]
