Problem 69 - Introductory Algebra for College Students

Question

Factor by grouping. $$x^{2}+2 x+4 x+8$$

Step-by-Step Solution

Answer

The factored expression is \((x+2)(x+4)\

Step 1: Group the terms

The given expression is \(x^{2}+2x+4x+8\). In the first step, rearrange and group the terms so they can be factored. Group the terms two by two: \((x^{2}+2x) + (4x+8)\).

Step 2: Factor out common factors within each group

Pull out common factors. From the first group \(x^{2}+2x\), x is common gives \(x(x+2)\). From the next group \(4x+8\), 4 is common which gives \(4(x+2)\). Now, the expression becomes \(x(x+2) + 4(x+2)\).

Step 3: Factor out the common binomial

There is a common binomial, \(x+2\), in both terms. Factor it out gives \((x+2)(x+4)\).