Write a polynomial that represents the length of each rectangle. Transcription: The area of the rectangle is 0.5x³ - 0.3x² + 0.22x + 0.06 square units and its width is x + 0.2 units

검증된 단계별 안내

Recall the formula for the area of a rectangle: \(\text{Area} = \text{Length} \times \text{Width}\).

Given the area as \(0.5x^{3} - 0.3x^{2} + 0.22x + 0.06\) and the width as \(x + 0.2\), set up the equation: \(0.5x^{3} - 0.3x^{2} + 0.22x + 0.06 = \text{Length} \times (x + 0.2)\).

To find the length, divide the area polynomial by the width polynomial: \(\text{Length} = \frac{0.5x^{3} - 0.3x^{2} + 0.22x + 0.06}{x + 0.2}\).

Perform polynomial division (either long division or synthetic division) to divide \(0.5x^{3} - 0.3x^{2} + 0.22x + 0.06\) by \(x + 0.2\).

The quotient from this division will be the polynomial expression representing the length of the rectangle.

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주요 개념

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

Polynomial Expressions

A polynomial is an algebraic expression consisting of terms with variables raised to non-negative integer powers and coefficients. Understanding how to manipulate polynomials, including addition, subtraction, multiplication, and division, is essential for working with expressions like the given area and width.

Area of a Rectangle

The area of a rectangle is found by multiplying its length by its width. Given the area and one dimension (width), you can find the other dimension (length) by dividing the area polynomial by the width polynomial.

Polynomial Division

Polynomial division is the process of dividing one polynomial by another, similar to numerical long division. It is used here to find the length polynomial by dividing the area polynomial by the width polynomial.

Write a polynomial that represents the length of each rectangle. Transcription: The area of the rectangle is 0.5x3 - 0.3x2 + 0.22x + 0.06 square units and its width is x + 0.2 units