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Chapter 0: Problem 51

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

Short Answer

Expert verified
The factorized form of the perfect square trinomial \(x^{2}-14x+49\) is \((x-7)^{2}\)

Step by step solution

01

Identify the trinomial

Firstly, identify that the provided expression \(x^{2}-14x+49\) is indeed a trinomial, because it has three terms.
02

Compare with standard perfect square trinomial form

The standard form of a perfect square trinomial is \(a^{2}-2ab+b^{2}\). Compare the given trinomial \(x^{2}-14x+49\) with this standard form. Here, \(a=x\), \(2ab=14x\) (which implies \(b=7\)), and \(b^{2}=49\). Therefore, the given trinomial can be expressed in the standard form.
03

Factor the trinomial

Given that this is a perfect square trinomial, it can be factored into \((a-b)^{2}\). Here, replacing \(a\) with \(x\) and \(b\) with \(7\), let's factorize \(x^{2}-14x+49\) into its factors: \((x-7)^{2}\)

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Most popular questions from this chapter

$$\text { Factor completely.}$$ $$y^{7}+y$$

Determine whether each statement in Exercises 43鈥�50 is true or false. $$-6>2$$

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Determine whether each statement in Exercises 43鈥�50 is true or false. $$0 \geq-6$$

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