Question

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)

1. 9
2. 24153
3. 11
4. 24109​

Answer 1

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