Question

Factorise x²+12/35x + 1/35

Answer 1

hey friend hope this will help you

Answer 2

Hi Bhoomi di,
Here is your answer.

 x2+12/35x+1/35 

Final result :

(7x + 1) • (5x + 1) ——————————————————— 35

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "x2"   was replaced by   "x^2". 

Step by step solution :

Step  1  :

1 Simplify —— 35

Equation at the end of step  1  :

12 1 ((x2) + (—— • x)) + —— 35 35

Step  2  :

12 Simplify —— 35

Equation at the end of step  2  :

12 1 ((x2) + (—— • x)) + —— 35 35

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Adding a fraction to a whole 

Rewrite the whole as a fraction using  35  as the denominator :
x2 x2 • 35 x2 = —— = ——————— 1 35
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole 

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

 3.2       Adding up the two equivalent fractions 
Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
x2 • 35 + 12x 35x2 + 12x ————————————— = —————————— 35 35

Equation at the end of step  3  :

(35x2 + 12x) 1 ———————————— + —— 35 35

Step  4  :

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   35x2 + 12x  =   x • (35x + 12) 

Adding fractions which have a common denominator :

 5.2       Adding fractions which have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
x • (35x+12) + 1 35x2 + 12x + 1 ———————————————— = —————————————— 35 35

Trying to factor by splitting the middle term

 5.3     Factoring  35x2 + 12x + 1 

The first term is,  35x2  its coefficient is  35 .
The middle term is,  +12x  its coefficient is  12 .
The last term, "the constant", is  +1 

Step-1 : Multiply the coefficient of the first term by the constant   35 • 1 = 35 

Step-2 : Find two factors of  35  whose sum equals the coefficient of the middle term, which is   12 .
     -35   +   -1   =   -36     -7   +   -5   =   -12     -5   +   -7   =   -12     -1   +   -35   =   -36     1   +   35   =   36     5   +   7   =   12   That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  5  and  7 
                     35x2 + 5x + 7x + 1

Step-4 : Add up the first 2 terms, pulling out like factors :
                    5x • (7x+1)
              Add up the last 2 terms, pulling out common factors :
                     1 • (7x+1)
Step-5 : Add up the four terms of step 4 :
                    (5x+1)  •  (7x+1)
             Which is the desired factorization

Final result :

(7x + 1) • (5x + 1) ——————————————————— 35



Some of it is copied from Google
With regards from
#@Jai