Question

what is the product?

(3x^5(2x^2 + 4x + 1))

• (2x^7 + 4x^6 + x^5)
• (6x^{10} + 12x^5 + 3x^5)
• (6x^7 + 12x^6 + 3x^5)
• (3x^5 + 2x^2 + 4x + 1)

Explanation:

Distribute the monomial to each term

$$ 3x^5(2x^2 + 4x + 1) = (3x^5 \cdot 2x^2) + (3x^5 \cdot 4x) + (3x^5 \cdot 1) $$

Apply exponent rules to multiply terms

$$
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$$

Combine the simplified terms

$$ 6x^7 + 12x^6 + 3x^5 $$

Answer:

• (A) \(2x^7 + 4x^6 + x^5\)
• (B) \(6x^{10} + 12x^5 + 3x^5\)
• (C) \(6x^7 + 12x^6 + 3x^5\) (Correct answer)
• (D) \(3x^5 + 2x^2 + 4x + 1\)