Question

what is the completely factored form of (f(x) = 6x^3 - 13x^2 - 4x + 15)?

• ((x + 1)(6x^2 - 19x + 15))
• ((x + 1)^2(2x - 3))
• ((x + 1)(3x - 2)(5x - 3))
• ((x + 1)(2x - 3)(3x - 5))

Explanation:

Test potential rational roots

Using the Factor Theorem knowledge point

$$
LATEXBLOCK0
$$

Thus, \(x + 1\) is a factor of \(f(x)\).

Divide the polynomial by the linear factor

Using the Polynomial Division knowledge point

$$
LATEXBLOCK1
$$

Factor the remaining quadratic expression

Using the Polynomial Factoring knowledge point

$$
LATEXBLOCK2
$$

Combine all factors

Using the Polynomial Factoring knowledge point

$$ f(x) = (x + 1)(2x - 3)(3x - 5) $$

Answer:

• (A) \((x + 1)(6x^2 - 19x + 15)\)
• (B) \((x + 1)^2(2x - 3)\)
• (C) \((x + 1)(3x - 2)(5x - 3)\)
• (D) \((x + 1)(2x - 3)(3x - 5)\) (Correct answer)