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Chapter 0: Problem 9

Factor out the greatest common factor. $$x^{2}(x-3)+12(x-3)$$

Short Answer

Expert verified
The factored form of the expression \(x^{2}(x-3)+12(x-3)\ is \( (x^{2} + 12)(x - 3).

Step by step solution

01

Identify the common factor

Look at each term in the problem to see what they have in common. In this case, both \(x^{2}(x-3)\) and \(12(x-3)\) share the \(x-3\) term.
02

Factor out the common factor

Factor out the common factor from both terms. Split the expression into two, by subtracting the common factor on both sides, \(x^{2}(x-3)+12(x-3) = (x - 3) \cdot x^{2} + (x - 3) \cdot 12\)
03

Combine like terms

We can now combine the two terms that are similar: \( (x - 3) \cdot x^{2} + (x - 3) \cdot 12 = (x^{2} + 12)(x - 3)
04

Write the final answer

Finally, write the answer as \( (x^{2} + 12)(x - 3), which is the factored form of the original expression \(x^{2}(x-3)+12(x-3)\).

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