Question

12x^2-35x+25 pls factorise this equation by splitting the middle term

Answer 1

Answer:

12x2+35x+25  

Final result :

 (4x + 5) • (3x + 5)

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 ((22•3x2) +  35x) +  25

Step  2  :

Trying to factor by splitting the middle term

2.1     Factoring  12x2+35x+25  

The first term is,  12x2  its coefficient is  12 .

The middle term is,  +35x  its coefficient is  35 .

The last term, "the constant", is  +25  

Step-1 : Multiply the coefficient of the first term by the constant   12 • 25 = 300  

Step-2 : Find two factors of  300  whose sum equals the coefficient of the middle term, which is   35 .

     -300    +    -1    =    -301  

     -150    +    -2    =    -152  

     -100    +    -3    =    -103  

     -75    +    -4    =    -79  

     -60    +    -5    =    -65  

     -50    +    -6    =    -56  

     -30    +    -10    =    -40  

     -25    +    -12    =    -37  

     -20    +    -15    =    -35  

     -15    +    -20    =    -35  

     -12    +    -25    =    -37  

     -10    +    -30    =    -40  

     -6    +    -50    =    -56  

     -5    +    -60    =    -65  

     -4    +    -75    =    -79  

     -3    +    -100    =    -103  

     -2    +    -150    =    -152  

     -1    +    -300    =    -301  

     1    +    300    =    301  

     2    +    150    =    152  

     3    +    100    =    103  

     4    +    75    =    79  

     5    +    60    =    65  

     6    +    50    =    56  

     10    +    30    =    40  

     12    +    25    =    37  

     15    +    20    =    35    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  15  and  20  

                    12x2 + 15x + 20x + 25

Step-4 : Add up the first 2 terms, pulling out like factors :

                   3x • (4x+5)

             Add up the last 2 terms, pulling out common factors :

                   5 • (4x+5)

Step-5 : Add up the four terms of step 4 :

                   (3x+5)  •  (4x+5)

            Which is the desired factorization

Final result :

 (4x + 5) • (3x + 5)

hope this helped you

pls mark as brainliest

thank you

merry christmas

Answer 2

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Here is your answer
Factorising by splitting the middle terms as

$12 {x}^{2} - 35x + 25 \\ = 12 {x}^{2} - 15x - 20x + 25 \\ = 3x(4x - 5) - 5(4x - 5) \\ = (4x - 5)(3x - 5)$

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