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.

Congratulations for Kanming Xu, Emily Xie, Claire Wang, Bryan Xian and Brian Gao. You are the winners from our class (Math 7A) in the 1st NCLS Math Competition.

The complete result is below.

Today we talked about solving equations in factored forms. A polynomial is said to be in factored form if it can be written in the product of two or more linear forms. With zero property, it becomes very easy to solve equations in such form, as all you need to do is to set each linear term to be zero and solve them one by one.

For quadratic functions, if they are in factored form, it also becomes easy to graph it, as we can quickly find out the two x-intercepts, which are the two solutions to the corresponding quadratic equation. The average of the two solutions’ x values gives the x value of the vertex. Plug that into the original function and you find out the y value for the vertex. With three points (2 x-intercepts and the vertex), you can quickly draw the parabola.

We then talked about how to factor a quadratical polynomial in the form of x^2 + bx + c. If it can be factored as (x+p)(x+q), then you have:

p + q = b

pq = c

That is, find two factors of c so that the sum is the same as b.

For homework, I handed out the WRONG one. Please download from the link below and print it out for your kid:

http://www.newtonchineseschool.org/teachers/wangweidong/HW4-3-2011.pdf

I handed last week’s math contest back to students and talked about a few of them in the class. If I have time in the future, I will talke some more.

Grade 6 and higher were doing M test, while Grade 5 and under were doing E test. We have 1 Grade 5 student who did quite well: 16 out of 31. We have 6 6th graders whose scores range from 13.5 (out of 29) to 1. We have 15 7th graders whose scores range from 21 (out of 29) to 3, and we have 2 8th graders whose scores range from 8 to 1.

All grade X students from across all math classes will be put together to pick the winners. I will have the final winners for you next week.

Note, this math contest is optional and is not part of the curriculum. For those who have not taken or gone to math Count or Math Olympia, they may find the questions hard to answer and don’t know how/where to start. Again, this is optional.