A polynomial of degree 3 has a double zero at 2. When x = 1 it takes the value 6 and when x = 3 it

takes the value 8. Find the polynomial.

p (x) = (x-2) ^2 (x+5)

Step-by-step explanation:

p (2) = 0 then p (x) = (x-2) ^2 (x-x1), x1=?

p (1) = 6

p (3) = 8

p (1) = (1-2) ^2 (1-x1)

6 = (-1) ^2 (1-x1)

6=1 (1-x1)

6=1-x1

x1=-5;

then p (x) = (x-2) ^2 (x - (-5)) = (x-2) ^2 (x+5)

Really: f (3) = (3-2) ^2 (3+5) = 1*8=8