Today we mainly focused on quadratic expression factorization (因式分解). This is a skill that is very useful in quickly solving quadratic equations. While it is not hard, it does take practice to get good at. So we spent most of the time letting the students going exercises.

Basically, for the simple form of x^2 + bx + c (that is, the coefficient in front of x^2 is 1) to be able to be factored as (x + p) (x + q), then p + q must be equal to b and pq (p times q) must be equal to c. So the basic steps are, first look at the factors for c and find two whose product is c, then check if their sum equals to b, if so, you have it. If not, try different pairs.

Then for the general form of ax^2 + bx + c (a <> 0), it is the same idea but a little more complicated. For it to be factored into (px + m)(qx + n), then pq (p times q) must be equal to a, mn( m times n) must be equal to c and pn + qm must be equal to b. The basic steps are, first look at the factors for a and pick two so that its product is a, then pick two factors of c so that its product is c, then check if the cross multiplication of those two pairs is b.

A cross multiplication chart will help

px         +m        | +pnx

X             |

qx          +n        | + qmx

—————————————-

pqx^2 + mn   | (pn + qm)x

With this skill, we looked at solving quadratic equations where we factor first.

Note, we have not got into the general solution of a quadratic equation yet.

Homework:

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