Question

which polynomial function (f(x)) has a leading coefficient of 1, roots (-4), (2), and (9) with multiplicity 1, and root (-5) with multiplicity 3?

(f(x) = 3(x + 5)(x + 4)(x - 2)(x - 9))
(f(x) = 3(x - 5)(x - 4)(x + 2)(x + 9))
(f(x) = (x + 5)(x + 5)(x + 5)(x + 4)(x - 2)(x - 9))
(f(x) = (x - 5)(x - 5)(x - 5)(x - 4)(x + 2)(x + 9))

Explanation:

Identify factors from roots

Using the Roots of Polynomials knowledge point

$$
LATEXBLOCK0
$$

Construct the polynomial function

Using the Roots of Polynomials knowledge point

$$
LATEXBLOCK1
$$

Match with given options

Using the Roots of Polynomials knowledge point

$$
LATEXBLOCK2
$$

Answer:

• f(x) = 3(x + 5)(x + 4)(x - 2)(x - 9)
• f(x) = 3(x - 5)(x - 4)(x + 2)(x + 9)
• f(x) = (x + 5)(x + 5)(x + 5)(x + 4)(x - 2)(x - 9) (Correct answer)
• f(x) = (x - 5)(x - 5)(x - 5)(x - 4)(x + 2)(x + 9)