Question

Considere o polinômio p(x)-4x4+3x3-2x2+x+k sabendo que p(1)=2, então o valor de k quando p(3) é:
a)386 b)405 c)324 d)81 e)368

Answer 1

p(x) = 4x4 + 3x3 -2x2 + x + k 

p(1)=2 ==>  4(1)4 + 3(1)3 -2(1)2 + 1 + k = 2

 4 + 3 - 2 + 1 + k = 2 ==> k = - 6 + 2 ==> k = - 4
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p(x) = 4x4 + 3x3 - 2x2 + x - 4

p(3) = 4(3)4 + 3(3)3 - 2(3)2 + 3 - 4==>  4(81) + 3(27) - 2(9) - 1

p(3) = 324 + 81 - 18 - 1 ==>  405 - 19 ==> 386

Answer 2

Substituindo P(1) = 2:

4(1)^{4} +3(1)^{3} -2(1)^{2}+1 +k=2=\ \textgreater \ k= \frac{1}{6}4(1)4+3(1)3−2(1)2+1+k=2= > k=61​

Assim, temos:

4(3)^{4}+3(3)^{3}-2(3)^{2}+3+ \frac{1}{6}+\ \textgreater \ 81+81-18+3+ \frac{1}{6}4(3)4+3(3)3−2(3)2+3+61​+ > 81+81−18+3+61​
147+ \frac{1}{6}=\ \textgreater \ \frac{883}{6}147+61​= > 6883​