If $(x - 2) . P (x) = 3 x^{3} + a x - 10$ $(x-2).P(x)= 3x^3+ax-10$ , what is $P (- 1)$ $P(-1)$ ?

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Answer 1 · 2016-06-05T15:11:03

From $(x - 2) P (x) = 3 x^{3} + a x - 10$ $(x-2)P(x)=3x^3+ax-10$ for $x = 2$ $x=2$ we get

$(2 - 2) P (2) = 3 \cdot 2^{3} + 2 a - 10 \Rightarrow 0 = 14 + 2 a \Rightarrow a = - 7$ $(2-2)P(2)=3*2^3+2a-10=>0=14+2a=>a=-7$

Hence the relation becomes

$(x - 2) P (x) = 3 x^{3} - 7 x + 10$ $(x-2)P(x)=3x^3-7x+10$

For $x = - 1$ $x=-1$ then

$(- 1 - 2) P (- 1) = - 3 + 7 + 10 \Rightarrow P (- 1) = - \frac{14}{3}$ $(-1-2)P(-1)=-3+7+10=>P(-1)=-14/3$

If (x-2).P(x)= 3x^3+ax-10(x−2).P(x)=3x3+ax−10(x-2).P(x)= 3x^3+ax-10 , what is P(-1)P(−1)P(-1) ?