Question

enter the correct answer in the box.

find the product.

\\((x + 9)(4x^2 + 5x + 6)\\)

Explanation:

⚡ Using what you learned: multiplying polynomials

Step 1: Distribute the terms

$$ (x + 9)(4x^2 + 5x + 6) = x(4x^2 + 5x + 6) + 9(4x^2 + 5x + 6) $$

Step 2: Expand each part

$$ x(4x^2 + 5x + 6) = 4x^3 + 5x^2 + 6x $$

$$ 9(4x^2 + 5x + 6) = 36x^2 + 45x + 54 $$

Step 3: Combine like terms

$$ 4x^3 + (5x^2 + 36x^2) + (6x + 45x) + 54 $$

$$ 4x^3 + 41x^2 + 51x + 54 $$

Answer:

\(4x^3 + 41x^2 + 51x + 54\)