Problem 66 Evaluate. $$ 1+x^{3}, \text ... [FREE SOLUTION]

Chapter 1: Problem 66

Evaluate. $$ 1+x^{3}, \text { for } x=-2 $$

Short Answer

Expert verified

The expression evaluates to -7 when x=-2.

Step by step solution

- Substitute the Value of x

Begin by substituting the given value of x, which is -2, into the expression. So substitute -2 for x in the expression 1 + x^3.

- Evaluate the Cubic Term

Next, evaluate the cubic term $x^3$ with x = -2. This means you need to find $(-2)^3$.

- Simplify the Cubic Term

Calculate $(-2)^3$. This equals -8 because $-2 \times -2 \times -2$ results in -8.

- Add the Simplified Cubic Term to 1

Add the simplified cubic term (-8) to 1. So, the expression becomes 1 + (-8).

- Simplify the Final Expression

Combine the numbers: 1 + (-8) = -7.

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Key Concepts

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

Substitution in Algebra

Substitution in algebra involves replacing a variable with a given number to evaluate an expression. For example, in the expression $1 + x^3$, we need to substitute $-2$ for $x$.

This means whenever we see $x$ in the expression, we replace it with $-2$. This substitution helps us to transform the algebraic expression into a numerical one, which is easier to solve.

For an expression $1 + x^3$ with $x = -2$, substitution changes it to $1 + (-2)^3$. This step is crucial because it sets up everything needed for evaluation.

Cubic Term Evaluation

Evaluating a cubic term means raising a number to the power of three. For instance, $x^3$ refers to multiplying $x$ by itself twice more. When $x = -2$, we need to calculate $(-2)^3$.

Here's the step-by-step process:

First, multiply $-2$ by itself: $-2 \times -2 = 4$
Then, multiply the result by $-2$ again: $-2 \times 4 = -8$

This gives us $(-2)^3 = -8$. The negative sign is important because an odd power of a negative number remains negative.

Expression Simplification

Expression simplification involves combining like terms and performing arithmetic operations. After evaluating the cubic term $(-2)^3$ to get $-8$, we replace $x^3$ in the expression $1 + (-2)^3$ with $-8$.

So, it becomes $1 + (-8)$. Simplify this by combining the two numbers:

1 + (-8) equals -7 because adding a negative number is the same as subtracting it.

Thus, the simplified expression $1 + x^3$ for $x = -2$ is \-7\. Simplification is the final step to get a clear numerical result from the algebraic expression.

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91影视

Evaluate. $$ 1+x^{3}, \text { for } x=-2 $$

Short Answer

Step by step solution

- Substitute the Value of x

- Evaluate the Cubic Term

- Simplify the Cubic Term

- Add the Simplified Cubic Term to 1

- Simplify the Final Expression

Key Concepts

Substitution in Algebra

Cubic Term Evaluation

Expression Simplification

One App. One Place for Learning.

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