Chapter 1.7, Problem 16E

Solution

To find: The value of $c$ that makes the expression $x^2-30x+c$ a perfect square trinomial, and write the expression as a square of binomial.

  $c=225$ ; ${\left(x-15\right)}^2$

Given information:

The expression $x^2-30x+c$ .

Concept used:

Perfect square formula: $a^2+2ab+b^2={\left(a+b\right)}^2$ ; $a^2-2ab+b^2={\left(a-b\right)}^2$ .

Calculation:

Rewrite the expression as follows:

  $x^2-30x+c=x^2-2\cdot x\cdot 15+c$

Here, $a=x$ and $b=15$ .

Then,

  $\begin{array}{c}c=b^2\\ ={15}^2\\ =255\end{array}$

So, the value of $c$ is 225.

Use the value of $c$ in the expression $x^2-30x+c$ and write a square of binomial.

  $\begin{array}{c}{x}^2-30x+225=x^2-2\cdot x\cdot 15+{15}^2\\ ={\left(x-15\right)}^2\end{array}$

Conclusion:

The value of $c$ is 225 and trinomial as a square of binomial is ${\left(x-15\right)}^2$ .