Question

select the correct answer.

what is the simplest form of this expression?

\\3x(-x^2 + 2x + 12)\\

• \\(-3x^3 + 5x^2 + 36x\\)
• \\(-3x^3 + 20x\\)
• \\(-3x^3 + 6x^2 + 36x\\)
• \\(-3x^3 + 5x^2 + 15x\\)

Explanation:

⚡ Using what you learned: multiplying polynomials

Step 1: Distribute the monomial

Multiply \( 3x \) by each term inside the parentheses:

$$ 3x(-x^2 + 2x + 12) = (3x \cdot -x^2) + (3x \cdot 2x) + (3x \cdot 12) $$

Step 2: Simplify each term

Apply the properties of exponents to simplify each product:

$$ 3x \cdot -x^2 = -3x^3 $$

$$ 3x \cdot 2x = 6x^2 $$

$$ 3x \cdot 12 = 36x $$

Combine the simplified terms:

$$ -3x^3 + 6x^2 + 36x $$

Answer:

\( -3x^3 + 6x^2 + 36x \) (the third option)