Factor Theorem & Synthetic Division...2

Section 2.3
Question 58



Since x = 2/3, (x - 2/3) is a factor of the given polynomial.

Using synthetic division, I got the following resulting coefficients: 48, -48, 9 with remainder 0.
This leads to 48x^2 - 48x + 9.

Factoring 48x^2 - 48x + 9, I got the following three factors: 3(3x - 1)(4x - 3).

The real solutions are: x = 1/4, x = 3/4.

You say?

 

48 x^3 - 80 x^2 + 41 x - 6 = ((48 x^2 - 48 x + 9))*(x - 2/3) + 0

48 x^2 - 48 x + 9=3(4x - 3) (4x - 1)

then

48 x^3 - 80 x^2 + 41 x - 6 =3(4x - 3) (4x - 1) (x - 2/3)

 

I factored incorrectly. I can now say that the real solutions are x = 2/3, x = 1/4, and x = 3/4.