Question

what are the factors of s^3 -3s +2? are they (s+2)^2 (s-2)? if so, how?​

Answer 1

Answer:

The answer to this question is (s-1) ^2 and (s-1)

Answer 2

Answer:

The factors of the equation s³ - 3s + 2 = 0 are (s - 1)²(s + 2).

Step-by-step explanation:

The equation is: s³ - 3s + 2 = 0.

Since the highest degree is 3, it is a 3-degree polynomial.

The first factor can be determined using the hit and trial method.

Put s = 1 in the above equation and check if the equation equals 0 or not.

$s^{3}-3s+2=0\\(1)^{3}-(3\times1)+2=0\\1-3+2=0\\0=0$

Thus, one of the factors is (s - 1).

Divide the equation by (s - 1).

$\frac{s^{3}-3s+2}{s-1}=s^{2}+\frac{s^{2}-3s+2}{s-1}=s^{2}+s+\frac{-2s+2}{s-1}=s^{2}+s-2$

Factorize the last equation as follows:

$s^{2}+s-2=0\\s^{2}+2s-s-2=0\\s(s+2)-1(s+2)=0\\(s-1)(s+2)=0$

Thus, the factors of the equation s³ - 3s + 2 = 0 are (s - 1)²(s + 2).