Problem 44 Find the value of each expressio... [FREE SOLUTION]

Chapter 11: Problem 44

Find the value of each expression. $$x^{2}+3 x-1, \text { if } x=5$$

Short Answer

Expert verified

The value is 39.

Step by step solution

Substitute the Value

Given the expression $x^2 + 3x - 1$, we need to find its value when $x = 5$. Start by substituting $5$ into the expression wherever there is an $x$. This gives us: $(5)^2 + 3(5) - 1$.

Evaluate the Square

Calculate $5^2$. Since $5^2 = 25$, replace $5^2$ with $25$, so the expression becomes: $25 + 3(5) - 1$.

Multiply

Next, multiply $3$ by $5$ to evaluate the middle term: $3 \times 5 = 15$. So, update the expression to $25 + 15 - 1$.

Simplify the Expression

Finally, perform the addition and subtraction from left to right. First, add $25$ and $15$ to get $40$, then subtract $1$ from $40$ to get $39$.

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Key Concepts

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

Substitution

Substitution is a useful technique in algebra that involves replacing a variable with a specific value. In the given expression, we are working with the variable $x$. The problem states that $x = 5$, so the substitution process requires us to replace each occurrence of $x$ in the expression with $5$. Start by rewriting the expression $x^2 + 3x - 1$ as $(5)^2 + 3(5) - 1$. This step is essential as it transforms an abstract mathematical expression into a numerical one that can be easily calculated. Substitution simplifies the evaluation process significantly by eliminating the variables, making direct computation possible.

Polynomial Evaluation

Polynomial evaluation involves calculating the value of a polynomial expression for a given value of the variable. In our exercise, the polynomial expression is $x^2 + 3x - 1$. After substitution, this becomes a numerical expression $(5)^2 + 3(5) - 1$.

Calculate the squared term: $(5)^2$ translates to $5 imes 5 = 25$.
Multiply the coefficient by the substituted value: $3 imes 5 = 15$.

Once you've done these calculations, you combine them together in the order they appear, giving a simplified numerical expression that can be easily computed.

Order of Operations

When evaluating expressions, it's crucial to follow the order of operations, often remembered by the acronym PEMDAS:

**P**arentheses
**E**xponents
**M**ultiplication and **D**ivision (from left to right)
**A**ddition and **S**ubtraction (from left to right)

In the given expression $(5)^2 + 3(5) - 1$, we first handle exponents: $(5)^2 = 25$. Next, perform multiplication: $3 imes 5 = 15$. Finally, carry out addition and subtraction from left to right: add $25$ and $15$ to get $40$, then subtract $1$ to end up with $39$.
By following this order, you ensure accurate and consistent results every time you evaluate polynomial expressions.

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91影视

Find the value of each expression. $$x^{2}+3 x-1, \text { if } x=5$$

Short Answer

Step by step solution

Substitute the Value

Evaluate the Square

Multiply

Simplify the Expression

Key Concepts

Substitution

Polynomial Evaluation

Order of Operations

One App. One Place for Learning.

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