Q9. - Algebra 1

Question

Determine whether each trinomial is a perfect square trinomial. Write yes or no. If so, factor it.

$x^2+5x+25$

Step-by-Step Solution

Answer

No, the given trinomial is not a perfect square trinomial.

Step 1. Observe the given trinomial x 2 + 5 x + 25 .

The given trinomial is: $x^2+5x+25$

The First, middle, and last terms of the given trinomial are $x^2,5x$ and 25 respectively.

The first term of the given trinomial can be written as:

$x^2={\left(x\right)}^2$

Therefore, the first term of the given trinomial is a perfect square.

The last term of the given trinomial can be written as:

$25={\left(5\right)}^2$

Therefore, the last term of the given trinomial is a perfect square.

The middle term of the given trinomial can be written as:

 $5x\ne 2\left(x\right)\left(5\right)$

Therefore, the middle term is not equal to twice the product of the square roots of the first term and last term.

Step 2. Determine whether the given trinomial x 2 + 5 x + 25 is a perfect square trinomial .

As the first and last terms of the given trinomial are a perfect square and the middle term is not equal to twice the product of the square roots of the first term and last term.

Therefore, No, the given trinomial is not a perfect square trinomial.