Question

factor the trinomial completely.

\\20x^3 + 38x^2 + 12x\\

\\6 = 1 \cdot 6, \quad 6 = 2 \cdot 3\\

now, try different combinations of factors of \\(10x^2\\) and \\(6\\) until a middle term of \\(19x\\) is obtained.

find the middle term.

\\(5x + 1)(2x + 6) = 10x^2 + \text{ } x + 6\\ (simplify your answer.)

Explanation:

⚡ Using what you learned: factoring trinomials

Step 1: Identify the terms to multiply

To find the middle term of the product \( (5x + 1)(2x + 6) \), we multiply the outer terms and the inner terms:

• Outer product: \( 5x \cdot 6 = 30x \)
• Inner product: \( 1 \cdot 2x = 2x \)

Step 2: Combine the terms

Add the outer and inner products together to find the middle term:

$$ 30x + 2x = 32x $$

Answer:

32