Question

1. find the factors of $x^2 - 6x + 9$ \

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a. $(x + 6)^2$ \
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b. $(x - 3)^2$ \
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c. $(x + 3)^2$ \
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d. $(x + 9)^2$

Explanation:

Step1: Recall the perfect square formula

The perfect square trinomial formula is \(a^2 - 2ab + b^2=(a - b)^2\).

Step2: Identify \(a\) and \(b\) in the given trinomial

For the trinomial \(x^2-6x + 9\), we have \(a = x\) (since \(x^2=a^2\)), and \(2ab=6x\). Substituting \(a = x\) into \(2ab = 6x\), we get \(2\times x\times b=6x\), which simplifies to \(2b = 6\), so \(b = 3\) (and \(b^2=9\), which matches the constant term).

Step3: Apply the perfect square formula

Using the formula \(a^2-2ab + b^2=(a - b)^2\) with \(a=x\) and \(b = 3\), we get \(x^2-6x + 9=(x - 3)^2\).

Answer:

B. \((x - 3)^2\)