Find the Roots (Zeros) P(x)=x^3+3x^2-4

Problem

P(x)=x^3+3*x^2−4

Solution

1. Identify potential rational roots using the Rational Root Theorem, which suggests testing factors of the constant term −4

2. Test the value x=1 by substituting it into the polynomial: 1^3+3*(1)^2−4=1+3−4=0

3. Conclude that (x−1) is a factor of P(x) since P(1)=0

4. Divide the polynomial x^3+3*x^2−4 by (x−1) using synthetic division or long division to find the remaining quadratic factor.

5. Result of the division is the quadratic x^2+4*x+4

6. Factor the quadratic expression x^2+4*x+4 which is a perfect square trinomial: (x+2)^2

7. Set each factor to zero to find the roots: x−1=0 and (x+2)^2=0

Final Answer

x=1,−2

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