Precalculus Examples

x^{2} + 2 x + 1

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

Step 1

A trinomial can be a perfect square if it satisfies the following:

The first term is a perfect square.

The third term is a perfect square.

The middle term is either

2

$2$ or

- 2

$- 2$ times the product of the square root of the first term and the square root of the third term.

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

${(a - b)}^{2} = a^{2} - 2 a b + b^{2}$

Step 2

Pull terms out from under the radical, assuming positive real numbers.

x

$x$

Step 3

Any root of

1

$1$ is

1

$1$ .

1

$1$

Step 4

The first term

x^{2}

$x^{2}$ is a perfect square. The third term

1

$1$ is a perfect square. The middle term

2 x

$2 x$ is

2

$2$ times the product of the square root of the first term

x

$x$ and the square root of the third term

1

$1$ .

The polynomial is a perfect square.

{(x + 1)}^{2}

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

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