Use the Rational Roots Test to Find All Possible Roots f(x)=x^3-10x^2+4x-24

Problem

ƒ(x)=x3−10*x2+4*x−24

Solution

1. Identify the constant term (a_0) and the leading coefficient (a_n) of the polynomial.

(a_0)=−24

(a_n)=1

2. List all integer factors of the constant term (a_0)=−24 which represent the possible values for p

p∈{±1,±2,±3,±4,±6,±8,±12,±24}

3. List all integer factors of the leading coefficient (a_n)=1 which represent the possible values for q

q∈{±1}

4. Apply the formula for the Rational Roots Test, which states that all possible rational roots are of the form p/q

p/q=(±1,±2,±3,±4,±6,±8,±12,±24)/(±1)

5. Simplify the list of possible rational roots by dividing each p by each q

Possible Roots∈{±1,±2,±3,±4,±6,±8,±12,±24}

Final Answer

Possible Roots=±1,±2,±3,±4,±6,±8,±12,±24

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