Erin is using this area model to factor 6x^2−7x−20 . She puts two terms in the upper left and lower right boxes.
The sum of the missing two terms in the area model must be
Answer Choices: (-7x, -20, 6x^2)
The missing two terms she is looking for are
(-13x, 7x. -15x, 8x. -6x, -x)
The expression factors to
Answer Choices:
(x - 4) (6x + 5)
(3x + 4) (2x - 5)
(3x - 4) (2x + 5)
(x + 4) (6x - 5)
The correct answer is (3x + 4) (2x - 5) because the missing two terms must add up to -7x and multiply to -20. In this case, the missing two terms are 3x and -15x, which add up to -7x and multiply to -45x. This creates the factored expression (3x + 4) (2x - 5).
what about the others
Let's check each combination:
1. (x - 4) (6x + 5)
The product of (x - 4) (6x + 5) is 6x^2 - 4x + 5x - 20 which simplifies to 6x^2 + x - 20.
2. (3x + 4) (2x - 5)
The product of (3x + 4) (2x - 5) is 6x^2 - 15x + 8x - 20 which simplifies to 6x^2 - 7x - 20.
3. (3x - 4) (2x + 5)
The product of (3x - 4) (2x + 5) is 6x^2 + 15x - 8x - 20 which simplifies to 6x^2 + 7x - 20.
4. (x + 4) (6x - 5)
The product of (x + 4) (6x - 5) is 6x^2 + 24x - 5x - 20 which simplifies to 6x^2 + 19x - 20.
Based on the original expression 6x^2 - 7x - 20, the correct factorization is (3x + 4) (2x - 5).