factoring polynomial 4x²-20x+25
Answers
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.