/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 12 Evaluate each polynomial for \(x... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 12

Evaluate each polynomial for \(x=2, y=-3,\) and \(z=-4\) $$ x y-x z+y z $$

Short Answer

Expert verified
14

Step by step solution

01

Substitute the values into the polynomial

Substitute the given values for the variables in the polynomial. For this exercise, substitute \(x = 2\), \(y = -3\), and \(z = -4\) into the polynomial expression \(xy - xz + yz\).
02

Calculate each term separately

Calculate the value of each term separately:1. \(xy\): Multiply \(x = 2\) and \(y = -3\).\[xy = 2 \times (-3) = -6\]2. \(xz\): Multiply \(x = 2\) and \(z = -4\).\[xz = 2 \times (-4) = -8\]3. \(yz\): Multiply \(y = -3\) and \(z = -4\).\[yz = -3 \times (-4) = 12\]
03

Combine the results

Now, combine the results of each term:\[ xy - xz + yz = -6 - (-8) + 12 \]When calculating, remember that subtracting a negative is the same as adding the positive.\[ -6 - (-8) + 12 = -6 + 8 + 12 = 14 \]

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.

Polynomial Substitution
Polynomial substitution is the process of replacing the variables in a polynomial with specific values. In our exercise, we are given the polynomial expression \(xy - xz + yz\) and we need to evaluate it by substituting \(x = 2\), \(y = -3\), and \(z = -4\).

This is how you do it:
  • Replace every instance of \(x\) with 2.
  • Replace every instance of \(y\) with -3.
  • Replace every instance of \(z\) with -4.
After substitution, the expression becomes: \[2(-3) - 2(-4) + (-3)(-4)\].

Once you substitute the values, you can start calculating each term separately.
Multiplication of Integers
Multiplying integers is a basic mathematical operation. Here, you are multiplying both positive and negative integers. Negative signs change the outcome.

Let's look into the steps again:
  • First, multiply \(2\) and \(-3\). Multiply the numbers as if they are positive, and then apply the negative sign: \[2 \times (-3) = -6\].
  • Next, we multiply \(2\) and \(-4\). Again, multiply the numbers first and then add the negative sign: \[2 \times (-4) = -8\].
  • Finally, multiply \(-3\) and \(-4\). Here, two negative signs make the product positive: \[-3 \times (-4) = 12\].
It helps to always check the signs of the numbers you are multiplying.
Combining Like Terms
Combining like terms means to simplify the expression by adding or subtracting coefficients of terms that have the same variables. In our scenario, after performing the multiplication, we get specific numerical results:

Our expression becomes: \[-6 - (-8) + 12\].

Notice that subtracting a negative like \(-(-8)\) means adding the positive:

\[-6 - (-8) = -6 + 8 = 2\].

The revised expression now is \[2 + 12\].

Finally, add the results of the remaining like terms:

\[2 + 12 = 14\].

So, the result for the given polynomial after substitution, multiplication, and combining like terms is \(14\).

It鈥檚 essential to follow these steps carefully to avoid errors.

One App. One Place for Learning.

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

Get started for free

Most popular questions from this chapter

Find the domain of \(F / G,\) if $$ F(x)=\frac{1}{x-4} \quad \text { and } \quad G(x)=\frac{x^{2}-4}{x-3} $$

Simplify. \(4 t^{4}+3 t^{2}+8 t-\left(3 t^{4}+9 t^{2}+8 t\right)\)

For each pair of functions \(f\) and \(g,\) determine the domain of \(f / g\) $$ \begin{aligned} &f(x)=\frac{2 x}{x+1}\\\ &g(x)=2 x+5 \end{aligned} $$

To prepare for Section \(5.2,\) review operations with integers (Sections \(1.5-1.7)\) Perform the indicated operations. $$ -16+5 $$

Find a value of the variable that shows that the two expressions are not equivalent. Answers may vary. $$ 3 x^{2} ;(3 x)^{2} $$
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Calculus

Read Explanation

Applied Mathematics

Read Explanation

Statistics

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.