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Chapter 0: Problem 51

Factor each perfect square trinomial. $$x^{2}-14 x+49$$

Short Answer

Expert verified
\((x-7)^{2}\)

Step by step solution

01

Identify the structure

The given trinomial is \(x^{2}-14x+49\). It fits the structure of a perfect square trinomial because it can be written in the form \(a^{2}-2ab+b^{2}\) where \(a=x\) and \(b=7\).
02

Factor the trinomial

A perfect square trinomial in the form \(a^{2}-2ab+b^{2}\) can be factored into \((a-b)^{2}\). Substituting \(a=x\) and \(b=7\), the factored form of the trinomial becomes \((x-7)^{2}\).

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