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Chapter 5: Problem 73

Find each product. In each case, neither factor is a monomial. $$(x+1)\left(x^{3}+2 x^{2}+3 x+4\right)$$

Short Answer

Expert verified
The product of \( (x+1)\) and \( \left(x^{3}+2 x^{2}+3 x+4\right) \) is \( x^{4}+3x^{3}+5x^{2}+7x+4 \)

Step by step solution

01

Apply the Distributive Property

To start, every term in the first expression should be multiplied by every term in the second expression. That would look like this: \(x(x^{3}+2x^{2}+3x+4) + 1(x^{3}+2x^{2}+3x+4)\)
02

Simplify Each Term

Simplify each of the terms created in the first step, which can be done as following: \(x^{4}+2x^{3}+3x^{2}+4x + x^{3}+2x^{2}+3x+4\)
03

Combining Like Terms

Finally, combine any like terms in the expression: \(x^{4}+3x^{3}+5x^{2}+7x + 4\). This gives the final products by multiplying two polynomials.

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Most popular questions from this chapter

Express \(\frac{7}{8}\) as a decimal. (Section \(1.3,\) Example 4 )

Solve: \(4 x-7>9 x-2 .\) (Section 2.7, Example 7)

Graph: \(y=\frac{1}{3} x+2 .\) (Section 3.4, Example 3)

Perform the indicated operations. $$(y+1)\left(y^{2}-y+1\right)-(y-1)\left(y^{2}+y+1\right)$$

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. Other than multiplying monomials, the distributive property is used to multiply other kinds of polynomials.
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