Question

What is the completely factored form of f(x) = 6x3 – 13x2 – 4x + 15?

Answer 1

Answer:

Option D is the correct answer.

Step-by-step explanation:

Answer 2

We have to determine the complete factored form of the given polynomial

$f(x)=6x^3-13x^2-4x+15$.

Let x= -1 in the given polynomial.

So, $f(-1)= 6(-1)^3-13(-1)^2-4(-1)+15 = -6-13+4+15 = 0$

So, by factor theorem

(x+1) is a factor of the given polynomial.

So, dividing the given polynomial by (x+1), we get quotient as $6x^2-19x+15$.

So, $6x^3-13x^2-4x+15$ = (x+1)$6x^2-19x+15$.

= $(x+1)(6x^2-10x-9x+15)$

=$(x+1)[ 2x(3x-5)-3(3x-5)]$

= $(x+1)(2x-3)(3x-5)$ is the completely factored form of the given polynomial.

Option D is the correct answer.