In Try This 3 you may have found that, when you are looking for a factor of a polynomial, you can try values that are factors of the constant term of the polynomial.
This is called the integral zero theorem. This theorem states that if x − a is a factor of a polynomial function P(x) with integral coefficients, then a is a factor of the constant term of P(x).1
Coming back to the example f(x) = 2x3 + 6x2 − 20x − 48, the factors of the constant term (−48) are ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±16, ±24, and ±48; so these are the numbers to test as a-values.
Complete questions 4.a., 4.c., and 4.e. on page 133 of the textbook. Answer
1 Adapted from Pre-Calculus 12. Whitby, ON: McGraw-Hill Ryerson, 2011. Reproduced with permission.