how can i explain factorization? And how to do it?

Question

I have to explain to a younger student how to do factorization, so i was wondering where to start!

I also need to factorize quadratics

Answer 1

Factorization is the beaking down of any number t otis multiples. That is 12 is broken down in to 3*4. 3 and 4 are the multiples of 12

Answer 2

Start with the most simple cases such as just factoring a number. Explain that every nuber has at least two factors ( itself and 1). So 7 = 7*1. If a number has only itself and 1 it is said to be prime.

Then show that every even number has 2 as factor so that the factors of 6 are 2*3 and so it is not prime. Show a number may have many factors such as 48 = 2*2*2*2*3.

Now discuss the disributive law a(b+c) = ab+ac.
For example, 2(3+5) = 2*3 + 2*5 = 16.
Show that 6+10 have the common factor 2 so it can be taken out and get 6+10 =2(3+5). You have factored out the common factor 2.

Then start introducing terms like x^2 +2x and show that x is a common factor so x^2+2x =x(x+2).

You can then get more advanced showing that x^2 -x +2 factors to (x-2)(x+1). Explain some of the more common factors such as (a+b)^2= a^2+2ab +b^2.

I don't know how young the student is, so you may want to go a little faster tha what I have suggested.

Good for you for helping this student.

Answer 3

First tell him/ her that factors are numbers multiplied together to get a certain # ( 3x4=12 { factors: 3 & 4}) Then start talking about how every # has at least two factors, 1 & the number itself. Mention that if there is two factors it is prime, like the # 13.Then talk about composites and how every even number , except for 2, is composite because it can be evenly divided by 2. Then start trying a couple # w/ that person. Easy ones like : 6- 1, 2,3,6 or 4- 1,2,4. But , make sure that that person knows his/ her multiplication facts.


Then you could probably start talking about prime factorization. Try making a factor tree and break it down until on the prime #s are left. ex: 144
/ \
12 12
/ \ / \
2 6 3 4
/\ /\
2 3 2 2
So the prime factorization of 144 would be 2x2x3x3x2x2, or in exponents, 2(4)x 3(2)=144

Answer 4

Get a bag of sweets, explain the concept of factorization, when the student gets a correct answer give one sweet as reward, then repeat for the reduced number, etc . Can even mention prime numbers.
If you don't want to use sweets use nuts sultanas etc
Divide up among family members, even the pets can be included

Answer 5

Hi,

I have master degree in mathematics and I have got thirteen ten years of teaching experience in Math at college level and currently I am working as a lecturer for an army engineering college author of math guide
contact me for solution .
thankyou

Answer 6

i remember they taught me PEMDAS
1.Parenthesis
2. exponents
3. multiplication
4. division
5.addition
6. subtraction

another way to remember pemdas is: Please Excuse My Dear Aunt Sallie