Answer:
p(x) = (x +2)(x +1)(x -3)
Step-by-step explanation:
Given p(x) = x³ -7x -6 has a factor of (x +1), you want the function written as a product of linear factors.
Remaining factors
Using synthetic division, we can divide p(x) by (x +1) to find the quadratic factor is (x² -x -6).
p(x) = (x +1)(x² -x -6)
To factor the quadratic, we note that the factor pairs of -6 are ...
-6 = -6(1) = -3(2)
The sum of divisors -3 and 2 is -1, so those will be the constants we need for the remaining binomial factors.
p(x) = (x +1)(x -3)(x +2)
