Question

factor the trinomial represented by the algebra tiles.
the factored trinomial is \boxed{}.
(type your answer in factored form.)

Explanation:

Step1: Identify the terms from tiles

We have 3 \(x^2\) tiles, 7 \(x\) tiles, and 2 \(1\) tiles. So the trinomial is \(3x^2 + 7x + 2\).

Step2: Factor the trinomial

We need two numbers that multiply to \(3\times2 = 6\) and add up to \(7\). The numbers are \(6\) and \(1\).
Rewrite the middle term: \(3x^2+6x + x + 2\)
Group the terms: \((3x^2 + 6x)+(x + 2)\)
Factor out common factors: \(3x(x + 2)+1(x + 2)\)
Factor out \((x + 2)\): \((3x + 1)(x + 2)\)

Answer:

\((3x + 1)(x + 2)\)