Erin is using this area model to factor 6x2−7x−20. She puts two terms in the upper left and lower right boxes.
6x2
−20
The product of the two terms shown in the area model is
120x
−120x^2
−120x
120x^2
To factor 6x^2 - 7x - 20 using the area model, we need to find two numbers that multiply to 6*(-20) = -120 and add up to -7.
The two numbers that satisfy these conditions are -15 and 8.
So, we rewrite the expression as:
6x^2 - 15x + 8x - 20
Now, we can factor by grouping:
(6x^2 - 15x) + (8x - 20)
3x(2x - 5) + 4(2x - 5)
(3x + 4)(2x - 5)
Therefore, the factors of 6x^2 - 7x - 20 are (3x + 4)(2x - 5).