Question

5x-4;3x+2;5x-4;3x+2​

Answer 1

Answer:

Step by step solution :

STEP

1

:

Equation at the end of step 1

 ((5 • (x4)) -  3x2) -  2  = 0  

STEP  

2

:

Equation at the end of step

2

:

 (5x4 -  3x2) -  2  = 0  

STEP

3

:

Trying to factor by splitting the middle term

3.1     Factoring  5x4-3x2-2  

The first term is,  5x4  its coefficient is  5 .

The middle term is,  -3x2  its coefficient is  -3 .

The last term, "the constant", is  -2  

Step-1 : Multiply the coefficient of the first term by the constant   5 • -2 = -10  

Step-2 : Find two factors of  -10  whose sum equals the coefficient of the middle term, which is   -3 .

     -10    +    1    =    -9  

     -5    +    2    =    -3    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -5  and  2  

                    5x4 - 5x2 + 2x2 - 2

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

                   5x2 • (x2-1)

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

                   2 • (x2-1)

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

                   (5x2+2)  •  (x2-1)

            Which is the desired factorization