Use the Rational Roots Test to Find All Possible Roots x^3-4x^2-7x+10

Problem

x3−4*x2−7*x+10

Solution

1. Identify the coefficients of the polynomial. The leading coefficient is (a_n)=1 and the constant term is (a_0)=10

2. List all factors of the constant term (a_0)=10 These are represented by p

p=±1,±2,±5,±10

3. List all factors of the leading coefficient (a_n)=1 These are represented by q

q=±1

4. Determine the possible rational roots by calculating all possible values of p/q Since q=±1 the possible roots are simply the factors of p

p/q=±1,±2,±5,±10

Final Answer

Possible Roots=±1,±2,±5,±10

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