Question

question 4 of 10
express the polynomial as a product of linear factors.
$f(x) = x^3 - 5x^2 - 18x + 72$

a. $(x - 3)(x + 3)(x - 8)$
b. $(x - 2)(x + 6)(x - 6)$
c. $(x - 3)(x + 4)(x - 6)$
d. $(x - 4)(x + 3)(x + 2)$

Explanation:

Step1: Test root x=3

$f(3)=3^3-5(3)^2-18(3)+72=27-45-54+72=0$, so (x-3) is a factor.

Step2: Divide polynomial by (x-3)

Use synthetic division: coefficients [1, -5, -18, 72] ÷ (x-3) gives quotient $x^2-2x-24$.

Step3: Factor quadratic

$x^2-2x-24=(x+4)(x-6)$.

Step4: Combine factors

$f(x)=(x-3)(x+4)(x-6)$.

Answer:

C. (x - 3)(x + 4)(x - 6)