Multiply each expression.
$-x(3x^2-4x+2)$

• A. $-3x^3+4x^2-2x$
• B. $3x^3-4x^2+2x$
• C. $-3x^3-4x^2-2x$
• D. $3x^3+4x^2+2x$

Answer: (A)

Verified step by step guidance

1. Identify the monomial and the polynomial in the expression you need to multiply. The monomial is a single term (like \$3x^2\(), and the polynomial is a sum of terms (like \)2x + 5$).
2. Apply the distributive property by multiplying the monomial by each term of the polynomial separately. This means you multiply the coefficients (numbers) together and then multiply the variables using the laws of exponents.
3. When multiplying variables with the same base, add their exponents. For example, \(x^a \times x^b = x^{a+b}\).
4. Write down each product from the distribution step as a separate term, keeping track of coefficients and variables with their new exponents.
5. Combine all the terms you found after distribution to write the final expression, which is the product of the monomial and the polynomial.