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Chapter 6: Problem 57

Factor each polynomial using the greatest common binomial factor. $$x(x+5)+3(x+5)$$

Short Answer

Expert verified
The polynomial \(x(x+5)+3(x+5)\) can be factored as \((x+5)(x+3)\).

Step by step solution

01

Identify the common binomial factor

In the given polynomial, the binomial \(x+5\) appears in both terms, \(x(x+5)\) and \(3(x+5)\). This tells us that the greatest common binomial factor is \(x+5\).
02

Factor out the common binomial factor

When \(x+5\) is factored out from the given polynomial, the expression will look something like this: \((x+5)(x+3)\). This is achieved by treating each of the terms \(x(x+5)\) and \(3(x+5)\) as the product of their binomial factors \(x\) and \((x+5)\), thus giving us \(x+(3)\), and arranging the expression accordingly.

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Most popular questions from this chapter

Now let's move on to factorizations that may require two or more techniques. Factor completely, or state that the polynomial is prime. Check factorizations using multiplication or a graphing utility. $$y^{3}+2 y^{2}-4 y-8$$

Factor completely. $$3 x^{5}-21 x^{3}-54 x$$

The second angle of a triangle measures three times that of the first angle's measure. The third angle measures \(80^{\circ}\) more than the first. Find the measure of each angle.

Factor: \(9 x^{2}-16 .\)

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