Factoring Polynomials and Dividing Polynomials

We started by factoring a quadratic without any instruction. Here are some photos of student work and my work. Some used a "short cut" and others used area = length * width.



 

Next we divided a cubic by a linear function. Some students wanted to use the long division algorithm but I encourage all to use the area = length * width model. We also verified that our solution was correct.

 

Here is some of the notes that I put on my whiteboard.

Next we talked about linear factors that divided in evenly would have a remainder of zero. Therefore if we can find a number that makes the function zero i.e. f(a) = 0 then x - a is a factor or f(a/b) = 0 then bx - a is a factor. Here are some examples with sketches of the graphs(three different questions). First one is my work.

 





 

We then went back and divided a Quartic by a quadratic to get a quadratic quotient and a linear remainder.