Question

Which polynomial represents a perfect square polynomial. Select all that apply

X^2+2x+1
X^2-2x+1
4x^2+12x+16
4x^2-12x-9

Answer 1

`{x}^(2) - 2x + 1`

and

`{x}^(2) + 2x + 1`

Step-by-step explanation

A perfect square trinomial can be written in the form:

`(a - b) ^(2) = {a}^(2) - 2(ab) + {b}^(2)`

or

`(a + b) ^(2) = {a}^(2) + 2(ab) + {b}^(2)`

For the first option;

`(x + 1) ^(2) = {x}^(2) + 2(x)(1)) + {1}^(2)`

This is a perfect square trinomial.

For the second option,

`(x - 1)^(2) = {x}^(2) - 2(x)(1)) + {1}^(2)`

This is also a perfect square trinomial.

The third option

`4 {x}^(2) + 12x + 16`

This cannot be written as a perfect square.

`4 {x}^(2) - 12x - 9`

This cannot also be written as a perfect square.