Question

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

Answer 1

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`

Answer 2

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`