Question

select the correct answer.

one factor of this polynomial is \\(x - 5\\)

\\x^3 - 15x^2 + 71x - 105\\

which expression represents the other factor, or factors, of the polynomial?

\\((x - 7)(x - 3)\\)

\\(x^2 + 10x + 21\\)

\\((x + 7)(x - 3)\\)

\\(x^2 + 10x - 21\\)

Explanation:

Divide the polynomial by the known factor

$$ \frac{x^3 - 15x^2 + 71x - 105}{x - 5} = x^2 - 10x + 21 $$

Factor the resulting quadratic expression

$$ x^2 - 10x + 21 = (x - 7)(x - 3) $$

Answer:

• (A) \((x - 7)(x - 3)\) (Correct answer)
• (B) \(x^2 + 10x + 21\)
• (C) \((x + 7)(x - 3)\)
• (D) \(x^2 + 10x - 21\)