In Exercises 15–58, find each product. (2x−3)(x2−3x+5)

Ch. P - Fundamental Concepts of Algebra

Blitzer8th EditionCollege AlgebraISBN: 9780136970514당신이 사용하는 게 아니라요?교과서 변경

모든 교과서

Blitzer 8th Edition

Ch. P - Fundamental Concepts of Algebra

문제 17

1장, 문제 17

In Exercises 15–58, find each product. (2x−3)(x²−3x+5)

검증된 단계별 안내

Step 1: Recognize that this is a multiplication of two polynomials, specifically a binomial (2x - 3) and a trinomial (x^2 - 3x + 5). To solve, use the distributive property (also known as the FOIL method for binomials).

Step 2: Distribute the first term of the binomial, 2x, to each term in the trinomial. This gives: (2x * x^2) + (2x * -3x) + (2x * 5).

Step 3: Simplify the terms from Step 2. This results in: 2x^3 - 6x^2 + 10x.

Step 4: Distribute the second term of the binomial, -3, to each term in the trinomial. This gives: (-3 * x^2) + (-3 * -3x) + (-3 * 5).

Step 5: Simplify the terms from Step 4 and combine them with the terms from Step 3. This results in: 2x^3 - 6x^2 + 10x - 3x^2 + 9x - 15. Combine like terms to simplify further.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Polynomial Multiplication

Polynomial multiplication involves distributing each term of one polynomial to every term of another polynomial. This process is often referred to as the distributive property, where you multiply each term in the first polynomial by each term in the second. For example, in the expression (2x−3)(x^2−3x+5), you would multiply 2x by each term in the second polynomial and then do the same for -3.

Combining Like Terms

After multiplying polynomials, the next step is to combine like terms, which are terms that have the same variable raised to the same power. This simplification process helps in reducing the expression to its simplest form. For instance, if the multiplication yields terms like 6x^2 and -3x^2, you would combine them to get 3x^2.

Standard Form of a Polynomial

The standard form of a polynomial is when the terms are arranged in descending order of their degrees. This means that the term with the highest exponent comes first, followed by the next highest, and so on. For example, a polynomial like 3x^2 + 2x - 5 is in standard form, which is important for clarity and further operations such as addition or comparison with other polynomials.