Question

factoring polynomial 4x²-20x+25​

Answer 1

Step-by-step explanation:

Factoring  4x2-20x+25 

The first term is,  4x^2  its coefficient is  4 .

The middle term is,  -20x  its coefficient is  -20 .

The last term, "the constant", is  +25 

Step-1 : Multiply the coefficient of the first term by the constant   4 • 25 = 100 

Step-2 : Find two factors of  100  whose sum equals the coefficient of the middle term, which is   -20 .

-10   +   -10   =   -20.

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -10  and  -10 

                     4x2 - 10x - 10x - 25

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

                    2x • (2x-5)

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

                    5 • (2x-5)

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

                    (2x-5)  •  (2x-5)

             Which is the desired factorization

2x-5 = 0 (or) 2x-5 = 0.

2x = 5 (or) 2x = 5.

x= 5/2 or x= 5/2.

therefore 4x²-20x+25 is having two equal roots...ie.,x= 5/2 or x= 5/2.