Answer
$(3q-7)(q+2)$
Work Step by Step
By solving using the box method, it makes it a lot easier to determine what numbers are used in the factorization. You place the first term in the upper left-hand corner and the third term in the bottom right-hand corner. Multiply those two terms and write the product off to the side out of the box. You need to find two numbers that have a product of the number calculated in the prior step, but also have a sum of the second term. Put the two values in the remaining openings (one in each) in the box and find the greatest common factor in each row and column:
![](https://gradesaver.s3.amazonaws.com/uploads/solution/d35c8f9e-8698-435b-8e29-647c0f1b9ede/steps_image/small_1545070626.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240908%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240908T000857Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=c0bcb5b001d3b8c150230d672a79d4c8c2113cb82525aa25dac44b8ab0b91c14)