Question

middle term factorisation of
15x2-5x-120​

Answer 1

Answer:

5 • (x - 3) • (3x + 8)

Step-by-step explanation

STEP

1

:

Equation at the end of step 1

 ((3•5x2) -  5x) -  120

STEP

2

:

STEP

3

:

Pulling out like terms

3.1     Pull out like factors :

  15x2 - 5x - 120  =   5 • (3x2 - x - 24)

Trying to factor by splitting the middle term

3.2     Factoring  3x2 - x - 24

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

The middle term is,  -x  its coefficient is  -1 .

The last term, "the constant", is  -24

Step-1 : Multiply the coefficient of the first term by the constant   3 • -24 = -72

Step-2 : Find two factors of  -72  whose sum equals the coefficient of the middle term, which is   -1 .

     -72    +    1    =    -71

     -36    +    2    =    -34

     -24    +    3    =    -21

     -18    +    4    =    -14

     -12    +    6    =    -6

     -9    +    8    =    -1    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -9  and  8

                    3x2 - 9x + 8x - 24

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

                   3x • (x-3)

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

                   8 • (x-3)

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

                   (3x+8)  •  (x-3)

            Which is the desired factorization

Final result :

 5 • (x - 3) • (3x + 8)