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If a polynomial is defined as P(x) = 2x5+ ax4+ bx3+ cx2+ dx + e such thatP(0) = 4,P(1) = 5,P(2) = 8,

P(3) = 13,P(4) = 20 find the value ofP(5).

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P(3) = 13,P(4) = 20 find the value ofP(5).

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P(0) = 4 => e = 4

P(1) = 5 => a+b+c+d = -1

P(2) = 8 => 8a + 4b + 2 c + d = -30

=> 7a + 3b + c = -29

P(3) = 13 => 27 a + 9 b + 3c +d = -159

=> 13 a + 4 b + c = -79

=> 6a + b = -50

P(4) = 20 => 64 a + 16 b + 4c + d = -508

=> 21a + 5 b + c = -169

=> 7a + b = -70

=> a = -20 and b = 70

then c = -99 and d = 48

P(5) = 6250 - 12500 + 8750 - 15 * 99 + 4 =__29__

P(1) = 5 => a+b+c+d = -1

P(2) = 8 => 8a + 4b + 2 c + d = -30

=> 7a + 3b + c = -29

P(3) = 13 => 27 a + 9 b + 3c +d = -159

=> 13 a + 4 b + c = -79

=> 6a + b = -50

P(4) = 20 => 64 a + 16 b + 4c + d = -508

=> 21a + 5 b + c = -169

=> 7a + b = -70

=> a = -20 and b = 70

then c = -99 and d = 48

P(5) = 6250 - 12500 + 8750 - 15 * 99 + 4 =