Question

divide x³-7x+6 by x+3​

Answer 1

Answer:

Step-by-step explanation:

   Polynomial Long Division

Dividing :  x3 - 7x - 6  

                             ("Dividend")

By         :    x - 3    ("Divisor")

dividend     x3      -  7x  -  6  

- divisor  * x2     x3  -  3x2          

remainder         3x2  -  7x  -  6  

- divisor  * 3x1         3x2  -  9x      

remainder             2x  -  6  

- divisor  * 2x0             2x  -  6  

remainder                0

Quotient :  x2+3x+2  Remainder:  0

or

The first term is,  x2  its coefficient is  1 .

The middle term is,  +3x  its coefficient is  3 .

The last term, "the constant", is  +2  

Step-1 : Multiply the coefficient of the first term by the constant   1 • 2 = 2  

Step-2 : Find two factors of  2  whose sum equals the coefficient of the middle term, which is   3 .

     -2    +    -1    =    -3  

     -1    +    -2    =    -3  

     1    +    2    =    3    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  1  and  2  

                    x2 + 1x + 2x + 2

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

                   x • (x+1)

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

                   2 • (x+1)

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

                   (x+2)  •  (x+1)

            Which is the desired factorization

Canceling Out :

1.4    Cancel out  (x-3)  which appears on both sides of the fraction line.

Final result :

 (x + 2) • (x + 1)

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