Find all the linear factors
f(x)=

x + 2

3x − 1

x − 2

Step-by-step explanation:

The order of the polynomial is 4, so there are 4 roots.

Use rational root theorem to find possible rational roots.

±1, ±2, ±4, ±8, ±1/3, ±2/3, ±4/3, ±8/3

By trial and error, -2, ⅓, and 2 are all roots.  The fourth root can't be imaginary (complex roots come in pairs), so one of the real roots must be repeated.

the factors are (x - 2)(x + 2)(3x - 1)

Step-by-step explanation:

The given polynomial function is expressed as

f(x) = 3x⁴ - 7x³ - 10x² + 28x - 8

The first step is to test for any value of x that satisfies the polynomial when

3x⁴ - 7x³ - 10x² + 28x - 8 = 0

Assuming x = 2, then

3(2)⁴ - 7(2)³ - 10(2)² + 28 × 2 - 8 = 0

48 - 56 - 40 + 56 - 8 = 0

0 = 0

It means that x - 2 is a factor.

To determine the other factors, we would apply the long division method. The steps are shown in the attached photo. Looking at the photo, we would factorize the quadratic equation which is expressed as

3x² + 5x - 2 = 0

3x² + 6x - x - 2 = 0

3x(x + 2) - 1(x + 2)

(3x - 1)(x + 2) = 0

c. 4 and 1/2 pounds is the answer! : )

the central idea is that:

individuals should refuse to cooperate with institutions they believe unjust.

thoreau felt  that governments were more often agents of corruption than justice, even democracies, and that just because the majority feels a certain way does not make it just or correct in absolute terms. he uses the fact that slavery exists in our democracy to support this idea.

he goes on to say that, as a result, people should live true to their own internal laws regarding right and wrong, as a product of reflection and a moral life, rather than following every law that society imposes. 

step-by-step explanation: