Use algebra tiles to factor each trinomial.
x^2+7x+12
To factor the trinomial x^2 + 7x + 12 using algebra tiles, we can model it using rectangular tiles.
First, we need to represent x^2 using a square tile.
| x | x |
| x | x |
Next, we need to represent 7x using rectangular tiles. Since the coefficient is positive, we use 7 positive x tiles.
| x | x | x | x | x | x | x |
| x | x | x | x | x | x | x |
Finally, we need to represent 12 using square and rectangular tiles. Since the coefficient is positive, we use 12 positive unit tiles.
| x | x | x | x | x | x | x | 1 | 1 | 1 | 1 | 1 | 1 |
| x | x | x | x | x | x | x | 1 | 1 | 1 | 1 | 1 | 1 |
We can arrange these tiles into a rectangle to represent the trinomial.
| x | x | x | x | x | x | x | 1 | 1 | 1 | 1 | 1 | 1 |
| x | x | x | x | x | x | x | 1 | 1 | 1 | 1 | 1 | 1 |
| x | x | x | x | x | x | x | 1 | 1 | 1 | 1 | 1 | 1 |
From this arrangement, we can see that the trinomial can be factored as:
(x + 3)(x + 4)