How do you determine whether #25x^2-60x+36# is a perfect square trinomial?

2 Answers
Aug 17, 2017

Answer:

Can the trinomial be factored into two identical binomials.

Explanation:

The answer is yes it can

# 25x^2 - 60 x + 36 = ( 5x -6) xx ( 5x -6)# so

# 25x^2 = 60x + 36 = (5x-6)^2#

Aug 17, 2017

Answer:

Look for the clues as described below.

Explanation:

If the trinomial is a perfect square trinomial, there will be some properties to check for.

#ax^2 +- bx + c#

  • both #a and c# must be perfect squares, with plus signs
  • check whether #b =2 xx sqrta xx sqrt c#

In this case: #a = 25 = 5^2" "and c= 36 = 6^2#

#2 xx sqrt25 xx sqrt 36 = 2 xx5xx6xx=60#
#b=60#

Therefore we know that #25x^2 -60x+25# is the square of a binomial.

It will factorise as:

#25x^2 -60x+25 = (5x-6)^2#