Q10. - Algebra 1

Question

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

 $x^2-12x+32$

Step-by-Step Solution

Answer

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

Step1. Given

$x^2-12x+32$

Step2. Observe the given trinomial x 2 − 12 x + 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 x 2 + 5 x + 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.