Problem 10

Question

Factor out the greatest common factor. $$x^{2}(2 x+5)+17(2 x+5)$$

Step-by-Step Solution

Verified
Answer
The factored form of the expression is \((2x + 5)(x^{2} + 17)\).
1Step 1: Identify the Common Factors
Looking at the expression, the common factors in both terms are \(2x+5\). The first term \(x^{2}(2 x+5)\) consists of this factor and \(x^{2}\), whereas the second term \(17(2 x+5)\) consists of \(2x+5\) with the factor \(17\) within it.
2Step 2: Factor Out the Common Factors
The next step is to factor out the common factor from both terms. This means that \(2x + 5\) will be separated from both terms and what will remain is \(x^{2}\) and \(17\).
3Step 3: Write the Final Expression
The final step is to write the factored form of the original expression. This is done by multiplying the factored-out \(2x + 5\) by the remaining terms. The final expression becomes \((2x + 5)(x^{2} + 17)\).