Question

is 6w^3 - 48w^2 - 30w + 240 factorisable???

Answer 1

Answer:

STEP 1 : Equation at the end of step 1

 ((2•3w2) -  30w) +  240

STEP 3 : Pulling out like terms

  Pull out like factors :

  6w2 - 30w + 24  =   6 • (w2 - 5w + 4)

 Factoring  w2 - 5w + 4  

The first term is,  w2  its coefficient is  1 .

The middle term is,  -5w  its coefficient is  -5 .

The last term, "the constant", is  +4  

Step-1 : Multiply the coefficient of the first term by the constant   1 • 4 = 4  

Step-2 : Find two factors of  4  whose sum equals the coefficient of the middle term, which is   -5 .

     -4    +    -1    =    -5    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -4  and  -1  

                    w2 - 4w - 1w - 4

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

                   w • (w-4)

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

                    1 • (w-4)

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

                   (w-1)  •  (w-4)

            Which is the desired factorization

=== 6 • (w - 1) • (w - 4)