Factor x^3-3x-2

Problem

x3−3*x−2

Solution

1. Test for roots using the Rational Root Theorem by checking divisors of the constant term −2 which are ±1 and ±2

2. Evaluate the polynomial at x=−1 (−1)3−3*(−1)−2=−1+3−2=0

3. Identify that since x=−1 is a root, (x+1) must be a factor of the polynomial.

4. Perform synthetic division or long division to divide x3−3*x−2 by (x+1)

5. Divide the coefficients (1,0,−3,−2) by the root −1 1 drops down, 1⋅(−1)=−1 0 + (-1) = -1,-1) \cdot (-1) = 1,3 + 1 = -2,-2) \cdot (-1) = 2,2 + 2 = 0$.

6. Write the resulting quadratic factor: x2−x−2

7. Factor the quadratic expression x2−x−2 into (x−2)*(x+1)

8. Combine all factors to get the final factored form: (x+1)*(x+1)*(x−2)

Final Answer

x3−3*x−2=(x+1)2*(x−2)

Want more problems? Check here!