Question

simplify the following expression.
$(4x^2 + x + 3)(x + 2)$
$?x^3 + \quadx^2 + \quadx + \quad$

Explanation:

Step1: Apply distributive property (FOIL for polynomials)

Multiply each term in the first polynomial by each term in the second polynomial:
$$(4x^2)(x) + (4x^2)(2) + (x)(x) + (x)(2) + (3)(x) + (3)(2)$$

Step2: Simplify each product

Simplify each term:
$$4x^3 + 8x^2 + x^2 + 2x + 3x + 6$$

Step3: Combine like terms

Combine the \(x^2\) terms, \(x\) terms:

• For \(x^2\): \(8x^2 + x^2 = 9x^2\)
• For \(x\): \(2x + 3x = 5x\)

So the simplified expression is:
$$4x^3 + 9x^2 + 5x + 6$$

Answer:

For the \(x^3\) term, the coefficient is \(4\); for \(x^2\) it's \(9\); for \(x\) it's \(5\); and the constant term is \(6\). So filling in the boxes:
\(4\) \(x^3 +\) \(9\) \(x^2 +\) \(5\) \(x +\) \(6\)

(If only the coefficient of \(x^3\) is asked based on the green box, the answer is \(4\).)