Problem 36 Find the value of \(3 x^{2}+8 x+... [FREE SOLUTION]

91影视

Beginning Algebra

Margaret L. Lial, John Hornsby

$Math Studyset 91影视 Explanations$ Math

11 Edition

Chapter 3: Problem 36

Find the value of $3 x^{2}+8 x+5$ for each given value of $x.$ $$ -1 $$

Short Answer

Expert verified

Step by step solution

Substitute the value of x

We are given the value of $ x = -1 $. Substitute $ x $ into the given quadratic expression: $ 3x^2 + 8x + 5 $.

Calculate $ x^2 $

First, calculate $ (-1)^2 $. Since $ (-1)^2 = 1 $, replace $ x^2 $ with 1 in the expression.

Multiply by coefficients

Next, multiply the squared value by the coefficient. So, $ 3(-1)^2 = 3 \times 1 = 3 $.

Calculate $ 8x $

Now, calculate $ 8 \times (-1) $. This gives $ 8 \times -1 = -8 $.

Add the constant term

The constant term in the expression is 5. Add this to the other calculated terms.

Sum the terms

Finally, add all the terms together: $ 3 + (-8) + 5 $. This simplifies to $ 3 - 8 + 5 = 0 $.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Substitution in Algebra

Substitution in algebra is like replacing a variable with its given value. Imagine you have a recipe, but instead of flour, it just says 'x'. If someone tells you 'x' is 2 cups of flour, you replace 'x' with 2 in your recipe. In algebra, if we're given a quadratic expression like $3x^2 + 8x + 5$ and told $x = -1$, we substitute $-1$ for $x$.
This makes our equation easier to work with. The original quadratic equation turns into $3(-1)^2 + 8(-1) + 5$. At this point, all our variables are numbers, which is simpler to solve.

Quadratic Expressions

Quadratic expressions are polynomial expressions where the variable is squared ($x^2$). The general form is $ax^2 + bx + c$. Here, $a$, $b$, and $c$ are constants, meaning they don't change. In the exercise, the quadratic expression is $3x^2 + 8x + 5$.
This means:

$a = 3$ (the coefficient before $x^2$)
$b = 8$ (the coefficient before $x$)
$c = 5$ (the constant term).

We use quadratic expressions to model relationships where one variable depends on the square of another, like projectile motion or areas of shapes.

Arithmetic Operations

Arithmetic operations include basic math: addition, subtraction, multiplication, and division. For the given quadratic expression, let's break down each operation:

**Squaring**: First, we calculate $(-1)^2$. This means multiplying $-1$ by itself, which gives $1$.
**Multiplication**: We then multiply 3 by $-1$ squared: $3 \times 1 = 3$. Next, multiply 8 by $-1$ to get $-8$.
**Addition and Subtraction**: Finally, add these results to the constant term: $3 + -8 + 5$. It's like balancing amounts. Combine and simplify to find the result, which is $0$.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Find the value of \(3 x^{2}+8 x+5\) for each given value of \(x.\) $$ -1 $$

Short Answer

Step by step solution

Substitute the value of x

Calculate \( x^2 \)

Multiply by coefficients

Calculate \( 8x \)

Add the constant term

Sum the terms

Key Concepts

Substitution in Algebra

Quadratic Expressions

Arithmetic Operations

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Mechanics Maths

Pure Maths

Geometry

Theoretical and Mathematical Physics

Applied Mathematics

Study anywhere. Anytime. Across all devices.