Question

question 2 of 5

select all the correct answers.

consider this polynomial.

\\(p(x) = 3x^3 + 11x^2 - 4x - 6\\)

which statements are true?

\\((x + 2)\\) is a factor of \\(p\\).

the quotient of \\(p(x)\\) and \\((x + 2)\\) is \\(3x^2 + 5x - 14 + \frac{22}{x + 2}\\).

\\(p(-2) = 22\\)

\\(p(-2) = 6\\)

the quotient of \\(p(x)\\) and \\((x + 2)\\) is \\(3x^2 + 5x + 6 + \frac{6}{x + 2}\\).

Explanation:

Evaluate the polynomial at \(x = -2\)

$$
LATEXBLOCK0
$$

Perform synthetic division of \(p(x)\) by \(x + 2\)

$$
LATEXBLOCK1
$$

Formulate the quotient and remainder expression

$$ \frac{p(x)}{x+2} = 3x^2 + 5x - 14 + \frac{22}{x+2} $$

Answer:

• \((x + 2)\) is a factor of \(p\).
• The quotient of \(p(x)\) and \((x + 2)\) is \(3x^2 + 5x - 14 + \frac{22}{x+2}\). (Correct answer)
• \(p(-2) = 22\) (Correct answer)
• \(p(-2) = 6\)
• The quotient of \(p(x)\) and \((x + 2)\) is \(3x^2 + 5x + 6 + \frac{6}{x+2}\).