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Chapter 0: Problem 4

Factor out the greatest common factor. $$4 x^{2}-8 x$$

Short Answer

Expert verified
The factored form of the expression \(4x^{2}-8x\) is \(4x(x - 2)\).

Step by step solution

01

Identify the Greatest Common Factor (GCF)

Review each term in the expression \(4x^{2}-8x\) and what they have in common. In this case, both terms, \(4x^{2}\) and \(8x\), are divisible by \(4x\). Thus, \(4x\) is the Greatest Common Factor (GCF).
02

Factor Out the Greatest Common Factor

To factor out the GCF from the original expression, divide each term of the original expression by the GCF. This gives us: \[(4x^{2}-8x) / 4x = x - 2\] Hence, the factored form of the expression is \(4x(x - 2)\).

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Most popular questions from this chapter

This will help you prepare for the material covered in the next section. If 6 is substituted for \(x\) in the equation $$2(x-3)-17=13-3(x+2)$$ is the resulting statement true or false?

Perform the indicated operations. $$\frac{1}{x^{n}-1}-\frac{1}{x^{n}+1}-\frac{1}{x^{2 n}-1}$$

Perform the indicated operations. Simplify the result, if possible. $$\left(\frac{1}{a^{3}-b^{3}} \cdot \frac{a c+a d-b c-b d}{1}\right)-\frac{c-d}{a^{2}+a b+b^{2}}$$

Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. An elevator at a construction site has a maximum capacity of 2800 pounds. If the elevator operator weighs 265 pounds and each cement bag weighs 65 pounds, how many bags of cement can be safely lifted on the elevator in one trip?

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$\frac{x^{2}-25}{x-5}=x-5$$
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