Use algebra tiles to factor each trinomial.
x^2+6x+5
To factor the trinomial x^2 + 6x + 5 using algebra tiles, we need to find two binomials that multiply to give the trinomial.
First, we represent the x^2 term using a square tile.
[ x^2 ][ x ]
Next, we represent the 6x term using a rectangle (2 tiles wide and 3 tiles long) by placing it below the square tile.
[ x^2 ][ x ]
[ x ][ x ][ x ][ x ][ x ][ x ]
Finally, we represent the constant term (5) as 5 individual unit tiles placed below the rectangle.
[ x^2 ][ x ]
[ x ][ x ][ x ][ x ][ x ][ x ]
[ 1 ][ 1 ][ 1 ][ 1 ][ 1 ]
To factor the trinomial, we need to arrange the tiles into two groups such that each group represents a binomial:
[ x^2 ][ x ][ 1 ][ 1 ]
[ x ][ x ][ x ][ x ][ x ]
We can see that one binomial is (x + 1), represented by the square tile and the two unit tiles.
The other binomial is (x + 5), represented by the rectangle and the three unit tiles.
Therefore, the factored form of x^2 + 6x + 5 is (x + 1)(x + 5).