How do you solve 2x^2+8x-24

2 • (x + 2) • (x - 6)

Step by Step Solution:

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STEP:

Equation at the end of step 1

 (2x2 -  8x) -  24

STEP:2

STEP:3

Pulling out like terms

3.1     Pull out like factors :

  2x2 - 8x - 24  =   2 • (x2 - 4x - 12)

Trying to factor by splitting the middle term

3.2     Factoring  x2 - 4x - 12

The first term is,  x2  its coefficient is  1 .

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

The last term, "the constant", is  -12

Step-1 : Multiply the coefficient of the first term by the constant   1 • -12 = -12

Step-2 : Find two factors of  -12  whose sum equals the coefficient of the middle term, which is   -4 .

     -12    +    1    =    -11

     -6    +    2    =    -4    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -6  and  2

                    x2 - 6x + 2x - 12

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

                   x • (x-6)

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

                   2 • (x-6)

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

                   (x+2)  •  (x-6)

            Which is the desired factorization

Final result :

 2 • (x + 2) • (x - 6)

m∠a is 90°

m∠b is 40°