Factor f(x)=x^3-x^2-17x-15

Problem

x3−x2−17*x−15

Solution

1. Identify potential roots using the Rational Root Theorem, which suggests testing factors of the constant term −15 (such as ±1,±3,±5.

2. Test the value x=−1 by substituting it into the polynomial: (−1)3−(−1)2−17*(−1)−15=−1−1+17−15=0

3. Apply the Factor Theorem, which states that since ƒ*(−1)=0 (x+1) is a factor of the polynomial.

4. Divide the polynomial x3−x2−17*x−15 by (x+1) using synthetic division or long division to find the remaining quadratic factor.

5. Calculate the quotient: (x3−x2−17*x−15)÷(x+1)=x2−2*x−15

6. Factor the resulting quadratic expression x2−2*x−15 by finding two numbers that multiply to −15 and add to −2 which are −5 and 3

7. Combine all factors to write the completely factored form of the polynomial.

Final Answer

x3−x2−17*x−15=(x+1)*(x−5)*(x+3)

Want more problems? Check here!