If p(x) is a polynomial of degree 3 with leading coefficient 1006. Also p(1)=1, p(2)=3, p(3)=5. What is the
value of p(5):
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here is three graphs of your solution hope it helps you
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Answer:
p(5) = 24153
Step-by-step explanation:
Given:
p(x) = 1006x³ + ax² + bx + c
for some a, b and c.
Then...
3p(1) - 8p(2) + 6p(3)
= 3×1006 + 3a + 3b + 3c
- 8×8×1006 - 32a - 16b - 8c
+ 6×27×1006 + 54a + 18b + 6c
= 101×1006 + 25a + 5b + c.
So...
p(5) = 125×1006 + 25a + 5b + c
= 24×1006 + 101×1006 + 25a + 5b + c
= 24×1006 + 3p(1) - 8p(2) + 6p(3)
= 24×1006 + 3 - 24 + 30
= 24144 + 9
= 24153
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