how factorization useful in solving problems in polynomials

Question

dumbcow · Answer

factoring is very helpful in both solving polynomials for zeros and in simplifying rational expressions

anonymous · Answer

can you say in brief with examples

compassionate · Answer

It's helpful when solving quadratic equations, too. Also, it makes the equation easier to work with and easier to read.

anonymous · Answer

in brief can you please say sir

compassionate · Answer

For example, if I had $$x^2 - 4$$


(x + 2)(x - 2) 
That's the factored version. It's much easier to read. Also, I can use it to solve for 0. 

x = -2 and x = 2, are my zero points. 
Factoring is a great way to simply things.

anonymous · Answer

thankyou

anonymous · Answer

ok first think of this

(x-a)*(x-b)=0     

in order for it to be true   
(x-a)  has to be 0  or x-b has to be zero.

polynomials can usually be factored into a (x-a)*(x-b) form and a and b 
 
Example:
(x-2)*(x-3)= 0   

(x-2) has to equal 0 or x-3 has to equal zero

if x=2 then
((2)-2)*(x-3)= 0
0*(2-3)=0  no matter  what it will still be zero

and 3 will also work
(x-2)*(3-3)=0
(3-2)*(0)=0   so both   2 and 3 will make it work. 
---

so any polynomial

can be factored  to a 
(x-a)*(x-b)*(x-c)*(x-d)...   and so on and so on

with just one a b c d... that works  then that is a zero.

anonymous · Answer

It stems from the fact that 
n1*n2*n3*n4*n5...   

with just 1  n =0 makes the whole thing =0  and therefore true.