Math, asked by gpk7699, 1 year ago

Middle term split of n(square)- 43n+463

Answers

Answered by Anonymous
3

Answer:

Step-by-step explanation:

n2+n-462=0  

Two solutions were found :

n = 21

n = -22

Step by step solution :

Step  1  :

Trying to factor by splitting the middle term

1.1     Factoring  n2+n-462  

The first term is,  n2  its coefficient is  1 .

The middle term is,  +n  its coefficient is  1 .

The last term, "the constant", is  -462  

Step-1 : Multiply the coefficient of the first term by the constant   1 • -462 = -462  

Step-2 : Find two factors of  -462  whose sum equals the coefficient of the middle term, which is   1 .

     -462    +    1    =    -461  

     -231    +    2    =    -229  

     -154    +    3    =    -151  

     -77    +    6    =    -71  

     -66    +    7    =    -59  

     -42    +    11    =    -31  

     -33    +    14    =    -19  

     -22    +    21    =    -1  

     -21    +    22    =    1    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -21  and  22  

                    n2 - 21n + 22n - 462

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

                   n • (n-21)

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

                   22 • (n-21)

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

                   (n+22)  •  (n-21)

            Which is the desired factorization


gpk7699: Thanks but it's not only n it's 43n
Anonymous: then
Answered by Anonymous
2

n2+n-462=0  

Two solutions were found :

n = 21

n = -22

Step by step solution :

Step  1  :

Trying to factor by splitting the middle term

1.1     Factoring  n2+n-462  

The first term is,  n2  its coefficient is  1 .

The middle term is,  +n  its coefficient is  1 .

The last term, "the constant", is  -462  

Step-1 : Multiply the coefficient of the first term by the constant   1 • -462 = -462  

Step-2 : Find two factors of  -462  whose sum equals the coefficient of the middle term, which is   1 .

     -462    +    1    =    -461  

     -231    +    2    =    -229  

     -154    +    3    =    -151  

     -77    +    6    =    -71  

     -66    +    7    =    -59  

     -42    +    11    =    -31  

     -33    +    14    =    -19  

     -22    +    21    =    -1  

     -21    +    22    =    1    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -21  and  22  

                    n2 - 21n + 22n - 462

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

                   n • (n-21)

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

                   22 • (n-21)

Step-5 : Add up the four terms of step

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