Question

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

Answer 1

ANSWER

${x}^{2} - 2x + 1$

and

${x}^{2} + 2x + 1$

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.