15
QuizMultiple Choice

Polynomial Functions — Test

Question 15 • Algebra II

What is the completely factored form of f of x is equal to 6 x cubed minus 13 x squared minus 4 x plus 15 ?

Answer
A
open paren x plus 1 close paren squared times open paren 2 x minus 3 close paren
B
open paren x plus 1 close paren times open paren 2 x minus 3 close paren times open paren 3 x minus 5 close paren
C
open paren x plus 1 close paren times open paren 6 x squared minus 19 x plus 15 close paren
D
open paren x plus 1 close paren times open paren 3 x minus 2 close paren times open paren 5 x minus 3 close paren

Explanation

Substitute x = -1 into the polynomial: 6(-1)³ − 13(-1)² − 4(-1) + 15 = 0, so (x + 1) is a factor. Dividing gives 6x² − 19x + 15, which factors as (2x − 3)(3x − 5). Therefore, the completely factored form is (x + 1)(2x − 3)(3x − 5), choice D.

AI-written and checked against the verified answer.

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