Problem 513 Evaluate each polynomial for the... [FREE SOLUTION]

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Prealgebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2016 Edition

Chapter 10: Problem 513

Evaluate each polynomial for the given value. $$200 x-\frac{1}{5} x^{2} \text { when } x=0$$

Short Answer

Expert verified

The value of the polynomial when $x = 0$ is 0.

Step by step solution

Identify the Polynomial and Substitute the Value

The given polynomial is $200x - \frac{1}{5}x^2$. We are asked to evaluate this polynomial for $x = 0$. Substitute $x = 0$ into the polynomial.

Simplify the Polynomial

After substituting $x = 0$, the polynomial becomes: \[200(0) - \frac{1}{5}(0)^2\]. Simplify this expression.

Calculate the Result

$200(0)$ is 0 and $\frac{1}{5}(0)^2$ is also 0. So the expression simplifies to 0.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

substitution

Substitution is a fundamental concept in algebra. It involves replacing a variable in an equation or expression with a specific value.
For the polynomial evaluation problem, the substitution step is crucial to find a numerical answer.
Let's take the given polynomial: $200x - \frac{1}{5}x^2$.
When asked to evaluate for $x = 0$, we replace every $x$ in the expression with 0.
This is how we handle substitution in algebra.
It's important to ensure accuracy during substitution, as any mistake can lead to incorrect results.

simplification

Simplification is the process of reducing an expression or equation to its simplest form. After substitution, we often need to simplify to get a final, easy-to-understand answer.
For example, once we substitute $x = 0$ into our polynomial, it becomes: \[200(0) - \frac{1}{5}(0)^2\].
We simplify this by calculating the values:

200(0) equals 0
$\frac{1}{5}(0)^2$ also equals 0

polynomial

A polynomial is a mathematical expression consisting of variables, coefficients, and exponents.
Polynomials can have one or more terms.
In the provided exercise, the polynomial is $200x - \frac{1}{5}x^2$.
Understanding polynomials involves recognizing their structure and the role each part plays:

The coefficient is a number multiplied by the variable (e.g., 200 in 200x).
The variable is typically denoted by letters like x or y.
The exponent tells us how many times the variable is multiplied by itself (e.g., $x^2$).

By mastering polynomials, you can solve many types of algebraic problems more effectively.
Polynomials appear in various fields, including physics, engineering, and economics, making their understanding crucial.

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91影视

Evaluate each polynomial for the given value. $$200 x-\frac{1}{5} x^{2} \text { when } x=0$$

Short Answer

Step by step solution

Identify the Polynomial and Substitute the Value

Simplify the Polynomial

Calculate the Result

Key Concepts

substitution

simplification

polynomial

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