factoring polynomial expressions

it the way to revenue the two binomial times each other  that we father break down to one simplest polynomial, we need to find the simplest polynomial back to the factors.

1. Ex. = +24 x+16

but in the factoring polynomial, the question would be what the factor is the

+24 x+16

step 1, check could the terms be farther simplified  first, so  +24 x+16

step 2,  check the is the term realted to the commonly methods:

, , or 

step 3, = , +24 x= (12x )  +16=()

so the answer would be  

but how to solve a question that couldn’t be factored based on those 3 methods?

2. EX:   +9x+4

after make sure that the question couldn’t follow the commonly factory methods, then we could separate the middle term (9x) to two term, 5x and 4 X, in order to have the same factor with 1st and 3rd term ,the , and the 4.

step 1,  +5x+4x+4

step 2, find the common factor between the and 5x, and the 4x with 4. treat as two binomials. pick common factor out of the term , then put it in front of  brusket

5x(x+1),   4(x+1)

step 3 get the same factor between the binomials, it one of the factor of the polynomial

the left two terms which  in front of brisket , add them together is the other factor of the original polynomials’ factor.

step 4 ,(x+1) (5x+4) the answer is showed out