Lesson 5: Simon's Favorite Factoring Trick — Practice Questions

1. 1. To make the expression $xy + 5x + 6y$ factorable using Simon's Favorite Factoring Trick, what constant must be added? ___

2. 2. After adding the necessary constant, the expression $ab + 7a - 2b$ can be factored. What is the factored form?

   • A. $(a+7)(b-2)$
   • B. $(a-2)(b+7)$
   • C. $(a+2)(b-7)$
   • D. $(a-7)(b+2)$

3. 3. To factor the expression $pq - 8p - 3q$ using Simon's Favorite Factoring Trick, you must add the constant ___.

4. 4. Which expression is the factored form of $xy - 6x + 2y$ after applying Simon's Favorite Factoring Trick?

   • A. $(x+2)(y-6)$
   • B. $(x-2)(y+6)$
   • C. $(x+6)(y-2)$
   • D. $(x-6)(y+2)$

5. 5. The expression $mn + 9m - n$ is made factorable by adding a constant, resulting in the form $(m-1)(n+9)$. What constant was added? ___

6. 6. How many pairs of positive integers $(x, y)$ satisfy the equation $(x+3)(y+4) = 20$?

7. 7. Find the total number of integer solution pairs $(x, y)$ for the equation $(x-1)(y-2) = 7$.

8. 8. For which equation are there no positive integer solutions for $x$ and $y$?

   • A. (x+1)(y+1) = 9
   • B. (x+4)(y+5) = 24
   • C. (x+2)(y+3) = 12
   • D. (x+1)(y+2) = 6

9. 9. When finding all integer solutions for $(x-5)(y+2) = 10$, what is a required step?

   • A. Consider only positive factor pairs of 10.
   • B. Consider both positive and negative factor pairs of 10.
   • C. Assume $x$ and $y$ must be positive.
   • D. Solve the equation $x-5=0$ or $y+2=0$.

10. 10. Given that $x$ and $y$ are integers that satisfy $(x-3)(y-5) = 14$, what is the largest possible value of $x$? $x = $ ___