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Chapter 0: Problem 17

Find each product. $$(2 x-3)\left(x^{2}-3 x+5\right)$$

Short Answer

Expert verified
Thus, the product of the given polynomials is \(2x^{3} - 9x^{2} + 19x - 15\).

Step by step solution

01

Distribute the First Term of the First Polynomial

First, distribute the first term of the first polynomial, \(2x\), to each term in the second polynomial. This results in \(2x * x^{2} = 2x^{3}\), \(2x * -3x = -6x^{2}\), and \(2x * 5 = 10x\).
02

Distribute the Second Term of the First Polynomial

Next, distribute the second term of the first polynomial, \(-3\), to each term in the second polynomial. This results in \(-3 * x^{2} = -3x^{2}\), \(-3 * -3x = 9x\) and \(-3 * 5 = -15\).
03

Combine Like Terms

Combine the terms from steps 1 and 2 that are similar (have the same variables and exponents). Thus, \(2x^{3}\) has no similar term, \(-6x^{2}\) and \(-3x^{2}\) add to \(-9x^{2}\), and \(10x\) and \(9x\) add to \(19x\). The constant \(-15\) remains as it is.

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