Practice Factoring Trinomials with Two Variables

1. Teron and Abigail were each asked to factor the quadratic expression \(-y^2-4y+12\). Their responses are shown below.

   Teron: \(-1(y-6)(y+2)\)
   

   Abigail: \((-y+6)(y-2)\)
   

   Which student wrote an expression that is equivalent to \(-y^2-4y+12\)?

   Choose 1 answer:

   1. Only Teron
   2. Only Abigail
   3. Both Teron and Abigail

   4. Neither Teron nor Abigail

2. The polynomial expressions ‍\(12y^3-5y^2-3y\) and \(5(3y+1)(2y-3)\) share a common binomial factor.

   What binomial factor do they share?

3. The quadratic expression ‍\(x^2+Mx+30\) can be factored as ‍\((x+a)(x+b)\), where ‍\(M\), ‍‍\(a\), ‍and ‍\(b\) are integers.

   Jusna wrote that ‍\(M\) could be equal to -13.

   Ethan wrote that \(M\) could be equal to ‍11.
   

   Which student is correct ?
   

   Choose 1 answer:

   1. Only Jusna
   2. Only Ethan
   3. Both Jusna and Ethan

   4. Neither Jusna nor Ethan

4. The rectangle below has an area of \(12ax-28ay+15bx-35by\) square meters and a width of \(4a+5b\) meters.

   What expression represents the length of the rectangle?

   
   

Source: Khan Academy, https://www.khanacademy.org/math/algebra-home/alg-polynomials/alg-factoring-polynomials-quadratic-forms/e/factoring_polynomials_with_two_variables
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License.