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Chapter 0: Problem 55

Factor each perfect square trinomial. $$9 x^{2}-6 x+1$$

Short Answer

Expert verified
The factored form of \(9 x^{2}-6 x+1\) is \((3x-1)^2\).

Step by step solution

01

Identify the Trinomial as Perfect Square

Check if the given trinomial \(9 x^{2}-6 x+1\) fits the formula \(a^{2}-2ab+b^{2}\). In this case, \(a=3x\), \(b=1\) since \(3x^{2} = 9x^{2}\), \(2*3x*1 = 6x\) and \(1^{2} = 1\). As the trinomial fits the formula, we can be sure that it is a perfect square trinomial.
02

Write it as Perfect Square

Since the trinomial fits the perfect square trinomial formula \(a^{2}-2ab+b^{2}\), it can be written as \((a-b)^2\). Therefore, we can write \(9 x^{2}-6 x+1\) as \((3x-1)^2\).
03

Factor

The final step to factor the perfect square is to rewrite the equation based on your work in step 2. For this problem, the factored form of \(9 x^{2}-6 x+1\) is \((3x-1)^2\).

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Most popular questions from this chapter

Determine whether each statement is trueor false. If the statement is false, make the necessary change(s) toproduce a true statement. $$x^{2}+36=(x+6)^{2}$$

a. A mathematics professor recently purchased a birthday cake for her son with the inscription $$\text { Happy }\left(2^{\frac{5}{2}} \cdot 2^{\frac{3}{4}} \div 2^{\frac{1}{4}}\right) \text { th Birthday. }$$ How old is the son? b. The birthday boy, excited by the inscription on the cake, tried to wolf down the whole thing. Professor Mom, concerned about the possible metamorphosis of her son into a blimp, exclaimed, "Hold on! It is your birthday, so why not take \(\frac{8^{-\frac{4}{3}}+2^{-2}}{16^{-\frac{3}{4}}}\) of the cake? I'll eat half of what's left over." How much of the cake did the professor eat?

Factor Completely. $$y^{7}+y$$

What does it mean to factor completely?

Evaluate each expression. $$ \sqrt[3]{\sqrt{\sqrt{169}+\sqrt{9}}+\sqrt{\sqrt[3]{1000}+\sqrt[3]{216}}} $$
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