Problem 59 - Introductory Algebra for College Students

Question

Factor each polynomial using the greatest common binomial factor. $$x(x+2)-4(x+2)$$

Step-by-Step Solution

Answer

The factored form of the polynomial \(x(x+2)-4(x+2)\) is \((x+2)(x-4)\).

Step 1: Identify Common Factor

The first thing to note in this process is that each term of the polynomial contains the binomial factor \(x+2\). This is our common factor.

Step 2: Factor out the Common Binomial

The next step is to factor out the common binomial factor. This means each term will be divided by the binomial, and we're left with \(x-4\). Hence, \((x+2)\) is multiplied by \(x-4\) to get the given expression.

Step 3: Write the Final Factored Form

Lastly, simply rewrite the polynomial in its factored form using parentheses in this way: \((x+2)(x-4)\).