Question

3x3 – 5x2 – 11x - 3 by (x – 3)​

Answer 1

Answer:

Step-by-step explanation:

i assume you gave a polynomial and your question is

$3x^{3} -5x^{2} -11x-3$ should be divided by x-3

Polynomial Long Division

Dividing :  3x3-5x2-11x-3  

                             ("Dividend")

By         :    x-3    ("Divisor")

dividend     3x3  -  5x2  -  11x  -  3  

- divisor  * 3x2     3x3  -  9x2          

remainder         4x2  -  11x  -  3  

- divisor  * 4x1         4x2  -  12x      

remainder             x  -  3  

- divisor  * x0             x  -  3  

remainder                0

Quotient :  3x2+4x+1  Remainder:  0

Factoring  3x2+4x+1  

The first term is,  3x2  its coefficient is  3 .

The middle term is,  +4x  its coefficient is  4 .

The last term, "the constant", is  +1  

Step-1 : Multiply the coefficient of the first term by the constant   3 • 1 = 3  

Step-2 : Find two factors of  3  whose sum equals the coefficient of the middle term, which is   4 .

     -3    +    -1    =    -4  

     -1    +    -3    =    -4  

     1    +    3    =    4    That's it

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

                    3x2 + 1x + 3x + 1

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

                   x • (3x+1)

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

                    1 • (3x+1)

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

                   (x+1)  •  (3x+1)

            Which is the desired factorization

Final result :

 (3x + 1) • (x + 1) • (x - 3)