Step 2: Use the Rational Root Theorem to find possible rational roots. The possible rational roots are the factors of the constant term (-6) divided by the factors of the leading coefficient (1).
Step 3: List the factors of -6: ±1, ±2, ±3, ±6.
Step 4: Test each possible rational root by substituting them into p(x) to see if they equal zero.
Step 5: Use synthetic division to divide p(x) by any root found in Step 4 to simplify the polynomial.
Step 6: Repeat the process with the resulting polynomial until all roots are found.
Step 7: Conclude that p(x) has three distinct real roots based on the results from synthetic division.
Polynomial Roots – Understanding the nature and number of roots of a polynomial function.
Rational Root Theorem – A method to identify possible rational roots of a polynomial.
Synthetic Division – A technique used to divide polynomials and find roots.
