Question

this is equation split middle term . no spam plzzz i want full solutioun no guess plz

Answer 1

this is your answer.☺️☺️

Answer 2

The first term is,  a2  its coefficient is  1 .

The middle term is,  -23a  its coefficient is  -23 .
The last term, "the constant", is  +120 

Step-1 : Multiply the coefficient of the first term by the constant   1 • 120 = 120 

Step-2 : Find two factors of  120  whose sum equals the coefficient of the middle term, which is   -23 .

     -120   +   -1   =   -121     -60   +   -2   =   -62     -40   +   -3   =   -43     -30   +   -4   =   -34     -24   +   -5   =   -29     -20   +   -6   =   -26     -15   +   -8   =   -23   That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -15  and  -8 
                     a2 - 15a - 8a - 120

Step-4 : Add up the first 2 terms, pulling out like factors :
                    a • (a-15)
              Add up the last 2 terms, pulling out common factors :
                    8 • (a-15)
Step-5 : Add up the four terms of step 4 :
                    (a-8)  •  (a-15)
             Which is the desired factorization

Equation at the end of step  1  : (a - 8) • (a - 15) = 0 Step  2  :Theory - Roots of a product :

 2.1    A product of several terms equals zero. 

 When a product of two or more terms equals zero, then at least one of the terms must be zero. 

 We shall now solve each term = 0 separately 

 In other words, we are going to solve as many equations as there are terms in the product 

 Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation :

 2.2      Solve  :    a-8 = 0 

 Add  8  to both sides of the equation : 
                      a = 8 

Solving a Single Variable Equation :

 2.3      Solve  :    a-15 = 0 

 Add  15  to both sides of the equation : 
                      a = 15 

Supplement : Solving Quadratic Equation DirectlySolving  a2-23a+120  = 0 directly

Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula