Question

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

$x^2-12x+32$

Short answer

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

Step-by-step solution

Step1. Given

$x^2-12x+32$

Step2. Observe the given trinomial x2−12x+32.

The given trinomial is: $x^2-12x+32$

The first, middle, and last terms of the given trinomial are $x^2,-12x$and 32 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 is not a perfect square.

Step3. Determine whether the given trinomial x2+5x+25 is a perfect square trinomial.

As the first term of the given trinomial is a perfect square but the last term of the given trinomial is not a perfect square.

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