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Chapter 5: Problem 68

Find each product. In each case, neither factor is a monomial. $$(x+2)\left(x^{2}+x+5\right)$$

Short Answer

Expert verified
The product of the polynomials \((x+2)\) and \((x^{2}+x+5)\) is \(x^{3}+3x^{2}+7x+10\)

Step by step solution

01

Distribute the term

The first step is to distribute the term \(x\) in the first bracket to each of the terms in the second bracket. This will result in a new polynomial: \(x^{3}+x^{2}+5x\)
02

Distribute the term again

The second step is to distribute the term \(2\), which is the second term in the first bracket, to each of the terms in the second bracket. This gives another polynomial: \(2x^{2}+2x+10\)
03

Combine like terms

Finally, the last step is to combine the two polynomials obtained in Step 1 and Step 2 by adding the like terms. The terms that have the same degree of \(x\) are referred to as the 'like terms'. This simplifies the expression to the final product: \(x^{3}+3x^{2}+7x+10\)

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