Chapter 4.4, Problem 85S

To determine

Check whether the given trinomial is a perfect square or not.

Answer to Problem 85S

The given trinomial is a perfect square.

Explanation of Solution

Given:

The given trinomial is $x^2-12x+36$ .

Calculation:

For perfect trinomial, the first and last terms need to be perfect squares and the middle term needs to be twice the product of the square roots of the first and last terms.

In the given trinomial $x^2-12x+36$ ,

the first $\left(1\right)$ and last terms $\left(36\right)$ are perfect squares.

  $a=1,b=6$

Middle term $=2ab=2\cdot 1\cdot 6=12$

Check $\to$

Apply identity $x^2\pm 2xy+y^2={\left(x\pm y\right)}^2$

  $\begin{array}{l}{x}^2-2\cdot 1\cdot 6x+6^2\\ ={\left(x-6\right)}^2\end{array}$

Hence the given trinomial is a perfect square.