As zero remainder is received for the synthetic division by -4, x = -4 is zero and (x+4) is the factor of the given polynomial. However, the subsequent division by 2 produced the non-zero remainder. x=2 is not a zero.
a) For f(x) = 2x 3 -5x2-4x+3 from the Rational roots test we can suggest that +/-3 (multiple of the factor 3/2) can be the possible solutions. Using synthetic division we find that x=3 is a zero of the polynomial:
where P - starting amount,
n - quantity of years,
k - annual interest rate,
F - future amount.
c) To find F after 10 year, let n = 10:
F = 2000*e 10*0.08 = 2000 * 2.226 = $4, 451.08
d) Lets say the $2,000 starting amount will double after z years:
2,000*ez*0.08 = 4,000
ez*0.08 = 2
0.08z = ln 2
0.08z = 0.693
Thus, z = 8.66
$2,000 will double in 8.66