Perform each division. See Examples 7 and 8. (9y2+12y-5)/(3y)

Ch. R - Review of Basic Concepts

Lial13th EditionCollege AlgebraISBN: 9780136881063당신이 사용하는 게 아니라요?교과서 변경

모든 교과서

Lial 13th Edition

Ch. R - Review of Basic Concepts

문제 79

1장, 문제 79

Perform each division. See Examples 7 and 8. (9y²+12y-5)/(3y)

검증된 단계별 안내

Identify the expression to be divided: \(\frac{9y^{2} + 12y - 5}{3y}\).

Rewrite the division as separate terms by dividing each term in the numerator by the denominator: \(\frac{9y^{2}}{3y} + \frac{12y}{3y} - \frac{5}{3y}\).

Simplify each term individually by reducing coefficients and variables where possible: For example, simplify \(\frac{9y^{2}}{3y}\) by dividing 9 by 3 and \(y^{2}\) by \(y\).

Write the simplified terms together to form the final expression after division.

Check your work by ensuring that each term is fully simplified and that the expression is written in standard algebraic form.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

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

Polynomial Division

Polynomial division involves dividing one polynomial by another, similar to numerical division. In this problem, each term of the numerator polynomial is divided individually by the denominator, simplifying the expression step-by-step.

Simplifying Algebraic Expressions

Simplifying algebraic expressions means reducing them to their simplest form by performing operations like division, combining like terms, and canceling common factors. This helps in making the expression easier to understand and work with.

Properties of Exponents

When dividing terms with variables, the properties of exponents apply, such as subtracting exponents when dividing like bases. For example, dividing y² by y results in y^(2-1) = y, which is essential for correctly simplifying terms.