Problem 57 - Introductory Algebra for College Students

Question

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

Step-by-Step Solution

Answer

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

Step 1: 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 \(x+5\).

Step 2: 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.