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What is the factored form of the polynomial?

[tex]\[ x^2 - 12x + 27 \][/tex]

A. [tex]\((x + 4)(x + 3)\)[/tex]
B. [tex]\((x - 4)(x + 3)\)[/tex]
C. [tex]\((x + 9)(x + 3)\)[/tex]
D. [tex]\((x - 9)(x - 3)\)[/tex]

Sagot :

GinnyAnswer
Sure, let's factor the polynomial [tex]\(x^2 - 12x + 27\)[/tex] step-by-step.

1. Understand the Polynomial: We start with the quadratic polynomial [tex]\(x^2 - 12x + 27\)[/tex].

2. Identify the Coefficients: The polynomial is in the standard form [tex]\(ax^2 + bx + c\)[/tex], where [tex]\(a = 1\)[/tex], [tex]\(b = -12\)[/tex], and [tex]\(c = 27\)[/tex].

3. Find the Factors of the Constant Term: We need to find two numbers that multiply to [tex]\(27\)[/tex] and add up to [tex]\(-12\)[/tex].
- List the pairs of factors of [tex]\(27\)[/tex]: [tex]\((1, 27)\)[/tex], [tex]\((3, 9)\)[/tex], [tex]\((-3, -9)\)[/tex], etc.

4. Select the Correct Pair: From the pairs above, [tex]\((-3, -9)\)[/tex] multiply to [tex]\(27\)[/tex] and add up to [tex]\(-12\)[/tex].

5. Write the Factored Form:
- Using the numbers [tex]\(-3\)[/tex] and [tex]\(-9\)[/tex], we can write the factors of the polynomial as:
[tex]\[ (x - 3)(x - 9) \][/tex]

Thus, the factored form of the polynomial [tex]\(x^2 - 12x + 27\)[/tex] is [tex]\((x - 9)(x - 3)\)[/tex].

So, the correct answer is:
[tex]\[ (x - 9)(x - 3) \][/tex]
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