Question

creating perfect square trinomials
what values are needed to make each expression a perfect square trinomial?

• ( x^2 + 4x + square )
• ( x^2 - 10x + square )

Explanation:

Step1: Recall perfect square formula

A perfect square trinomial has the form \(x^{2}+bx + c=(x + \frac{b}{2})^{2}\), so \(c = (\frac{b}{2})^{2}\).

Step2: Solve for \(x^{2}+4x+\square\)

For \(x^{2}+4x+\square\), \(b = 4\). Then \(\frac{b}{2}=\frac{4}{2}=2\), and \(c = 2^{2}=4\).

Step3: Solve for \(x^{2}-10x+\square\)

For \(x^{2}-10x+\square\), \(b=- 10\). Then \(\frac{b}{2}=\frac{-10}{2}=-5\), and \(c=(-5)^{2}=25\).

Answer:

For \(x^{2}+4x+\square\), the value is \(4\); for \(x^{2}-10x+\square\), the value is \(25\).