Question

select the correct answer.

what is the simplest form of this expression?

(-x(4x^2 - 6x + 1))

• (-4x^3 - 6x^2 - x)
• (-4x^3 + 6x^2 - x)
• (-4x^3 - 6x + 1)
• (-4x^3 + 5x)

Explanation:

⚡ Using what you learned: multiplying polynomials

Step 1: Distribute the term

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

$$ -x(4x^2 - 6x + 1) = (-x)(4x^2) + (-x)(-6x) + (-x)(1) $$

Step 2: Simplify each term

Apply the rules of exponents and signs:

$$ (-x)(4x^2) = -4x^3 $$

$$ (-x)(-6x) = 6x^2 $$

$$ (-x)(1) = -x $$

Combine the simplified terms:

$$ -4x^3 + 6x^2 - x $$

Answer:

$$ -4x^3 + 6x^2 - x $$

(This corresponds to the second option)