Today we went over factoring a quadratic polymonial in the form of ax^2 + bx + c. Compared with the last lesson where we talked about factoring x^2 + bx + c, we are introducing the “a” (non 1) for the X
square term.

For it to be able to factor into the form of (mx + p)(nx + q), then:

a = mn
c = pq
b = mq + np

One way to work it out is to list the a’s factors m and n, along with c’s factors p and q in a matrix form:

m     p
X
n     q

The sum of of the cross-product mq + np must be equal to b.

We practiced this with several questions in the classroom. This will take some more practice to get good at.

We then talked about factoring out a polynomial completely. We talked about factoring a polynomial like the following:

x^3 -2x^2 -9x + 18
= x^2 (x – 2) -9(x – 2)
= (x – 2)(X^2 – 9)
= (x – 2)(x – 3)(x + 3)

We went over some more questions from the math contest.

There will be no school for the next two Sundays (4/17 and 4/24). Enjoy the Easter and the April break.