Use the Factor Theorem to find all real zeros for the given polynomial function and one factor. (Enter your answers as a comma-separated list.)

Question

f(x) = −3x³ + 10x² − 9;    x − 3

Answer 1

Yes, x-3 is factor and x=3 is a solution

because (-3)3^3 + 10(3^2) - 9 =

(-3)(27) + 10(9) - 9 =

-81 + 90 - 9 = 9-9=0

Synthetic division says:

3 | -3 10 0 -9

-9 3 9

___________________

-3 1 3 0

-3x^2 + x + 3 = 0

3x^2 -x - 3 = 0

x = [1 +or- sqrt( 1 + 4*3*3))]/ 6

= [ 1 +or- sqrt(37)]/6