how to teach factorization?

Quote:

Originally Posted by kenny1999

actually i am a teacher of junior maths, my students are mainly 13-14 years old

i need to teach a topic on factorization

but my students really can't master well with it.

I don't even think I explain to them very clearly, so I understand I have a problem, as a teacher

I can only push them to do more exercise and practice

but I really can't think of any skills or quick tips for them

can any one suggest how to teach factorization??

Hi kenny1999,

I will assume that you are talking about factoring quadratics, am I right?

A lot of teachers use the 'guess and check' method especially when the leading coefficient is 1. This takes a little more time when that coefficient is something other than 1.

Here's how I approach those. You might find it useful.

First a simple one: $2x^2+7x+3$

Step 1: Multiply the leading coefficient (2) times the constant (3) to get (6).

Step 2: Determine (mentally) what two factors make (6) that also add up to the middle coefficient (7). You can quickly come up with (6) and (1).

Step 3: Replace the original middle term with these two values from Step 2.

$2x^2+6x+1x+3$

Step 4: Factor by grouping

$2x(x+3)+1(x+3)$

$\boxed{(2x+1)(x+3)}$

Here's a second one: $6x^2+5x-6$

Step 1: 6 times -6 = -36

Step 2: With a little thinking, I can come up with -4 and 9 as my two factors that add up to +5.

Step 3: $6x^2-4x+9x-6$

Step 4: $2x(3x-2)+3(3x-2)$

$\boxed{(2x+3)(3x-2)}$

I hope this is helpful to you and your students. It works for mine.