Identifying Trinomials That Are Perfect Squares

a

4

b

12

c

9

reset

For the chosen coefficients, the trinomial a

2

x

+ bx + c =

4

2

x

+ 12x + 9

To see if the trinomial is a perfect square, check if

a

∈,

c

∈, and b2

a

c

:

2∈, 3∈, 12 = 2 × 2 × 3.

Therefore the trinomial is a perfect square:

4

2

x

+ 12x + 9 = ( 2x + 3

2

)

This Demonstration allows students and teachers to create trinomials of the form

a

2

x

+bx+c

, where

a

,

b

, and

c

are integers, and to check whether the trinomials are perfect squares.