SUMMARY
To find the x-intercept of the cubic polynomial function f(x) = x^3 + 3x^2 - 9x + 5, one must evaluate the integer factors of the constant term, which is 5. The relevant factors are +/-1 and +/-5. By substituting these values into the function, one can identify which yields zero. If f(1) = 0, then x = 1 is an x-intercept, and x - 1 is a factor, allowing for polynomial long division to find additional intercepts.
PREREQUISITES
- Cubic polynomial functions
- Integer factorization
- Polynomial long division
- Graphing techniques for functions
NEXT STEPS
- Learn polynomial long division techniques
- Study the Rational Root Theorem for polynomial equations
- Explore graphing cubic functions using graphing calculators or software
- Investigate synthetic division as an alternative to long division
USEFUL FOR
Students studying algebra, mathematics educators, and anyone interested in understanding cubic polynomials and their properties.