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Chapter 0: Problem 10

Factor out the greatest common factor. $$x^{2}(2 x+5)+17(2 x+5)$$

Short Answer

Expert verified
The factored form of the expression is \((2x + 5)(x^{2} + 17)\).

Step by step solution

01

Identify the Common Factors

Looking at the expression, the common factors in both terms are \(2x+5\). The first term \(x^{2}(2 x+5)\) consists of this factor and \(x^{2}\), whereas the second term \(17(2 x+5)\) consists of \(2x+5\) with the factor \(17\) within it.
02

Factor Out the Common Factors

The next step is to factor out the common factor from both terms. This means that \(2x + 5\) will be separated from both terms and what will remain is \(x^{2}\) and \(17\).
03

Write the Final Expression

The final step is to write the factored form of the original expression. This is done by multiplying the factored-out \(2x + 5\) by the remaining terms. The final expression becomes \((2x + 5)(x^{2} + 17)\).

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Most popular questions from this chapter

Find all integers b so that the trinomial can be factored. $$x^{2}+b x+15$$

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\frac{5}{4} \cdot \frac{8}{15}$$

Factor completely. $$(x-5)^{-\frac{1}{2}}(x+5)^{-\frac{1}{2}}-(x+5)^{\frac{1}{2}}(x-5)^{-\frac{3}{2}}$$

Describe what it means to rationalize a denominator. Use both \(\frac{1}{\sqrt{5}}\) and \(\frac{1}{5+\sqrt{5}}\) in your explanation.

What difference is there in simplifying \(\sqrt[3]{(-5)^{3}}\) and \(\sqrt[4]{(-5)^{4} ?}\)
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