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Chapter 0: Problem 74

Factor completely, or state that the polynomial is prime. $$6 x^{2}-6 x-12$$

Short Answer

Expert verified
The factored form of \(6 x^{2}-6 x-12\) is \(6(x-2)(x+1)\).

Step by step solution

01

Identify Common Factors

First look for any common factors in all terms of the polynomial. Each coefficient in \(6 x^{2}-6 x-12\) is divisible by 6.
02

Factor out the Common Factor

Factor out the common factor \(6\) from all terms to simplify the polynomial. This gives us \(6(x^{2}-x-2)\).
03

Factorize Further

Now factor the quadratic \(x^{2}-x-2\). The factors of -2 that sum up to -1 are -2 and 1. Thus the quadratic can be written as \((x-2)(x+1)\).
04

Write the Final Answer

Lastly combine step 2 and 3 for the final answer: The factored form of the original polynomial is \(6(x-2)(x+1)\).

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Most popular questions from this chapter

Perform the indicated operations. Simplify the result, if possible. $$\frac{a b}{a^{2}+a b+b^{2}}+\left(\frac{a c-a d-b c+b d}{a c-a d+b c-b d} \div \frac{a^{3}-b^{3}}{a^{3}+b^{3}}\right)$$

If you are given a quadratic equation, how do you determine which method to use to solve it?

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Explain how to solve \(x^{2}+6 x+8=0\) using the quadratic formula.

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