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Chapter 5: Problem 58

Find each product. In each case, neither factor is a monomial. $$(2 x+5)(x+3)$$

Short Answer

Expert verified
The product of the given binomial expressions is \( 2x^2 + 11x + 15 \)

Step by step solution

01

Distribute the first term from the first binomial

Multiply the first term in the first binomial by each term in the second binomial. This gives: \( 2x * x + 2x * 3 = 2x^2 + 6x \)
02

Distribute the second term from the first binomial

Now, multiply the second term in the first binomial by each term in the second binomial. This gives: \( 5 * x + 5 * 3 = 5x + 15 \)
03

Add together all the resulting terms

Combine the terms from Steps 1 and 2 to get the final answer: \( 2x^2 + 6x + 5x + 15 \)
04

Simplify the polynomial

Combine the like terms to get: \( 2x^2 + 11x + 15 \)

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