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Chapter 6: Problem 22

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. $$x^{2}+6 x$$

Short Answer

Expert verified
The factored form of the polynomial \(x^{2}+6 x\) is \(x(x+6)\).

Step by step solution

01

Identify Common Factors

Looking at the terms in this polynomial, \(x^{2}\) and \(6 x\), both terms have a common factor of \(x\).
02

Factor out the Common Factors

Use the distributive property, also known as factoring out, to separate the common factor. This means \(x^{2}+6 x\) equals \(x(x+6)\). We are essentially reversing the original distribution of \(x\) throughout \(x + 6\). It's just like saying that, 2*(3+4) is the same as 2*3 + 2*4. So, we are doing the same thing but in reverse.
03

Check Your Work

To ensure that the original polynomial was factored correctly, distribute \(x\) throughout \(x + 6\). This should result in the original polynomial \(x^{2}+6 x\).

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Most popular questions from this chapter

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

Factor completely. $$y^{7}+y$$

Contain polynomials in several variables. Factor each polynomial completely and check using multiplication. $$3 a^{2}+15 a b+18 b^{2}$$

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. $$\begin{aligned} &-2 x^{3}+10 x^{2}-2 x-10=2(x+5)\left(x^{2}+1\right) ;[-8,4,1] \text { by }\\\ &[-100,100,10] \end{aligned}$$

Contain polynomials in several variables. Factor each polynomial completely and check using multiplication. $$25 a^{2}+25 a b+6 b^{2}$$
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