Question

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

Explanation:

Step1: Identify the terms from the tiles

From the algebra tiles, we have:

• Number of \(x^2\) tiles: 3, so the \(x^2\) term is \(3x^2\).
• Number of \(x\) tiles: 7, so the \(x\) term is \(7x\).
• Number of constant (1) tiles: 4, so the constant term is \(4\).

So the trinomial is \(3x^2 + 7x + 4\).

Step2: Factor the trinomial

We need to find two binomials \((ax + b)(cx + d)\) such that \(ac = 3\), \(bd = 4\), and \(ad + bc = 7\).

Since \(ac = 3\), the possible values for \(a\) and \(c\) are \(a = 3\), \(c = 1\) (or vice - versa).

Now, we need to find \(b\) and \(d\) such that \(bd = 4\) and \(3d + b=7\).

The factor pairs of 4 are \((1,4)\), \((2,2)\), \((4,1)\), \(( - 1,-4)\), \((-2,-2)\), \((-4,-1)\).

Let's try \(b = 4\) and \(d = 1\): \(3\times1+4 = 3 + 4=7\), which works.

So the factored form is \((3x + 4)(x + 1)\).

Answer:

\((3x + 4)(x + 1)\)