Factoring trinomials using the area model

How can we determine the two binomials that multiply together to create the product 6x^2+17x+5?

We know that we can fill in the area model box, putting the squared term in the top left, and the constant in the bottom right spots. We need to now figure out what goes in the two empty spaces. We know that the sum of these two values is 17x and that the product is going to be 30x^2 (the product of “a”x”c”) in our trinomial ax^2+bx+c

After a bit of thinking/list making, we determine that the values of 15x and 2x should go into the boxes. We then look for common factors vertically and horizontally, which will be the factors.

This is the visual method of factoring trinomials using the area model.