Question

Given the polynomial
and one factor, which is
, find the solutions of thepolynomial function
.
(9 points)
x3 − 3x2 − 18x − 20 (x + 4)
f (x) = x3 − 3x2 − 18x + 40
x = -1
x = 1
x = -2
x = 2
x = -3
x = 3
x = -4
x = 4
x = -5
x = 5

Answer 1

We have f(x) = x^3 − 3x^2 − 18x + 40 and (x + 4) is a factor, so x = −4 is a root.

Divide f(x) by (x + 4) (synthetic division with −4):
coefficients 1, −3, −18, 40
bring down 1 → multiply −4 → −4 → add to −3 → −7 → multiply −4 → 28 → add to −18 → 10 → multiply −4 → −40 → add to 40 → 0

Quotient is x^2 − 7x + 10, which factors as (x − 5)(x − 2).

Therefore the solutions are x = −4, 2, 5.