Question

Factor completely: 5x3 + 15x2 + 10x

Answer 1

Answer:

 -5x • (x + 2) • (x + 1)

Step-by-step explanation:

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "x2"   was replaced by   "x^2".  1 more similar replacement(s).

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 ((0 -  (5 • (x3))) -  (3•5x2)) -  10x

Step  2  :

Equation at the end of step  2  :

 ((0 -  5x3) -  (3•5x2)) -  10x

Step  3  :

Step  4  :

Pulling out like terms :

4.1     Pull out like factors :

  -5x3 - 15x2 - 10x  =   -5x • (x2 + 3x + 2)  

Trying to factor by splitting the middle term

4.2     Factoring  x2 + 3x + 2  

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

Final result :

 -5x • (x + 2) • (x + 1)