Today we continued to cover the content of factorization, with focus on factoring ax^2 + bx + c.

If it can be factored, then we can write the following:

ax^2 + bx +c = (mx + p) (nx + q) = mnx^2 + (mq+np)x + pq

Then we have:

a = mn

b = mq + np

c = pq

That is, we want to find two factors m and n from a, so that a = mn, we want to find two factors p and q from c, so that c = pq, and such that the mq + np = b.

If you list m, n, p, q the following way:

m        p

X

n        q

It is the sum of the cross-product, m * q + n * p that must equal to b.

We also talked abut factoring by group. For example:

x^3 +2x^2 +3x +6 = x^2(x+2) + 3(x+2) = (x+2)(x^2 + 2)

Factorization takes time to get good at and only practice can get you there. So here is the homework:

http://blog.newtonchineseschool.org/wangweidong/files/2012/02/Math7_Spring_HW_L2.pdf