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Chapter 6: Problem 13

Factor each polynomial using the greatest common factor. If there is no common factor other than 1 and the polynomial cannot be factored, so state. $$8 x+8$$

Short Answer

Expert verified
The factored form of the polynomial \(8x + 8\) using the greatest common factor is \(8(x+1)\).

Step by step solution

01

Identify the GCF

The first step is to identify the greatest common factor (GCF) for \(8x\) and \(8\). Here, observe that the GCF between the coefficient of \(x\) which is \(8\), and the constant term which is \(8\), is \(8\). This is because \(8\) can divide both \(8x\) and \(8\) evenly.
02

Factor out the GCF

The next step is to factor out the greatest common factor (GCF) from each term in the polynomial. Here, the GCF is \(8\). Factoring this out from \(8x + 8\) we obtain \(8(x+1)\).

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Most popular questions from this chapter

Use the \([\mathrm{GRAPH}]\) or \([\mathrm { TABLE }]\) feature of a graphing utility to determine if the polynomial on the left side of each equation has been correctly factored. If not, factor the polynomial correctly and then use your graphing utility to verify the factorization. $$\begin{aligned} &x^{4}-16=\left(x^{2}+4\right)(x+2)(x-2) ;[-5,5,1] \text { by }\\\ &[-20,20,2] \end{aligned}$$

Exercises 150鈥�152 will help you prepare for the material covered in the next section. Evaluate \((3 x-1)(x+2)\) for \(x=\frac{1}{3}\)

Exercises 150鈥�152 will help you prepare for the material covered in the next section. Evaluate \(2 x^{2}+7 x-4\) for \(x=\frac{1}{2}\)

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