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

Verified step by step guidance

1. Identify the expression to be divided: \(\frac{9y^{2} + 12y - 5}{3y}\).
2. Rewrite the division as separate terms by dividing each term in the numerator by the denominator: \(\frac{9y^{2}}{3y} + \frac{12y}{3y} - \frac{5}{3y}\).
3. 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 \(y\).
4. Write the simplified terms together to form the final expression after division.
5. Check your work by ensuring that each term is fully simplified and that the expression is written in standard algebraic form.

Key Concepts

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.