SOLUTION: 8) Use the Rational Zero Theorem to list all possible rational zeros for the given function f(x) = - 2x ^ 3 + 3x ^ 2

SOLUTION: 8) Use the Rational Zero Theorem to list all possible rational zeros for the given function f(x) = - 2x ^ 3 + 3x ^ 2 - 4x + 8

Question 1168599: 8) Use the Rational Zero Theorem to list all possible rational zeros for the given function
f(x) = - 2x ^ 3 + 3x ^ 2 - 4x + 8
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!
Use the Rational Zero Theorem to list all possible rational zeros for the given function

Since all coefficients are integers, we can apply the rational zeros theorem.
The trailing coefficient (coefficient of the constant term) is .
Find its factors (with plus and minus): ±,±,±,±. These are the possible values for .
The leading coefficient (coefficient of the term with the highest degree) is .
Find its factors (with plus and minus): ±,±. These are the possible values for .
Find all possible values of :
±,±,±,±,±,±,±,±.
Simplify and remove duplicates (if any), these are rational roots: ±,±,±,±,±

Next, check the possible roots:
if is a of the polynomial , the remainder from the division of by should equal .
Check : divide by .The quotient is and the remainder is (use the synthetic division calculator to see the steps).
Check : divide by .The quotient is and the remainder is (use the synthetic division calculator to see the steps).
Check : divide by .The quotient is and the remainder is (use the synthetic division calculator to see the steps).
Check : divide by .The quotient is and the remainder is (use the synthetic division calculator to see the steps).
Check : divide by .The quotient is and the remainder is (use the synthetic division calculator to see the steps).
Check : divide by .The quotient is and the remainder is (use the synthetic division calculator to see the steps).
Check : divide by .The quotient is and the remainder is (use the synthetic division calculator to see the steps).
Check : divide by .The quotient is and the remainder is (use the synthetic division calculator to see the steps).
Check : divide by .The quotient is and the remainder is (use the synthetic division calculator to see the steps).
Check : divide by .The quotient is and the remainder is (use the synthetic division calculator to see the steps).

so, none of these possible rational roots ±,±,±,±,± are real roots of given function because long division by them does not gives us reminder

RELATED QUESTIONS
Use the rational zero theorem to list all possible rational zeros for the given function. (answered by Fombitz)

Use the rational zero theorem to list all possible rational zeros for the given function (answered by stanbon)

Use the Rational Zero Theorem to list all possible rational zeros for the given... (answered by solver91311)

Using the rational zeros theorem, list all possible rational zeros for the given... (answered by ReadingBoosters)

Use the Rational Zero Theorem to list all possible rational zeros for the given function. (answered by oscargut)

Use the Rational Zeros Theorem to write a list of all possible rational zeros of the... (answered by richwmiller)

Use the rational zero theorem to list all possible rational zeros for the given function. (answered by DrBeeee)

Use the rational zero theorem to list all the possible rational zeros of f(x). f(x)=... (answered by Fombitz)

Use the Rational Zero Theorem to list all possible rational zeros for the given function. (answered by lwsshak3)