Question

Choose the rows in which the polynomial expression is accurately described.

a) (4x - 9) - the cube of the difference of 4 × x and 9
b) (3y + 10)^2 - the difference of 3 × y and 10 raised to the exponent 2
c) (4x + 3)^2 / (x-10) - the quantity of the square of the sum of 4 × x and 3 divided by the difference of x and 10
d) (7x+7) - the sum of 8 × the square of y and 2 cubed

Answer 1

The polynomial expression that is accurately described is option c)
`\(((4x + 3)^2)/((x-10))\)` - the quantity of the square of the sum of
`\(4 * x\) and \(3\)` divided by the difference of \
`(x\) and \(10\).`

Step-by-step explanation:

Option c) accurately describes the given polynomial expression
`\(((4x + 3)^2)/((x-10))\).` It represents the quantity of the square of the sum of
`\(4 * x\) and \(3\)` divided by the difference of
`\(x\) and \(10\).` Mathematically, this is expressed as
`\(((4x + 3)^2)/((x-10))\),` where
`\((4x + 3)^2\)` denotes the square of the sum of
`\(4 * x\)` and \(3\), and \((x-10)\) represents the difference of
`\(x\) and \(10\).`

Understanding the structure of polynomial expressions and accurately interpreting their descriptions is crucial. In this case, the expression involves both addition and subtraction, and the proper use of parentheses ensures that the operations are carried out correctly. The numerator
`\((4x + 3)^2\)`signifies the square of the sum, and the denominator
`\((x-10)\)` represents the difference. This precise representation distinguishes option c) as the correct description of the polynomial.

Analyzing polynomial expressions requires attention to mathematical language and notation. Expressions can involve various operations, and accurately describing them is essential for proper understanding and manipulation. Option c) successfully captures the structure of the given polynomial expression, providing a clear and concise representation of the mathematical relationship between the terms.