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Adding and Subtracting Polynomials | MathHelp.com
By MathHelp.com
In this example, notice that each of our variables, x, y, and z, appears in all three equations. To solve this system, we use the addition method. In other words, let’s start with our first two equations, x + y + z = 4, and x – y + z = 2. Notice that if we add these equations together, the +y and –y will cancel out, and we have 2x + 2z = 6. So, in our new equation, 2x + 2z = 6, we’ve eliminated the variable y. Unfortunately, we still haven’t solved for any of our variables. However, if we can create another equation with just x and z in it, then we’ll have a system of equations in two variables, which we can use to solve for x and z. To create another equation with just x and z in it, we need to eliminate y. We can’t add the first and second equations together, because we’ve already done that. However, notice that if we add the first and third equations together, the first equation has a +y and the third equation has a –y, so we’ll be able to eliminate the y. So we have our first equation, x + y + z = 4, and our third equation, x – y – z = 0, and adding them together, notice that the +y – y cancels out, and, as a bonus, the +z – z also cancels out, so we have 2x = 4, and dividing both sides by 2, x = 2. Now, since we know that x = 2, notice that if we plug a 2 in for x in the equation that we created earlier, we can solve for z. And we have 2(2) + 2z = 6, or 4 + 2z = 6, and subtracting 4 from both sides, we have 2z = 2, and dividing both sides by 2, z = 1. So x = 2 and z = 1, and to find the value of y, we simply plug our values of x and z into any of the equations in the original system. Let’s use the first equation, x + y + z = 4. Since x = 2 and z = 1, we plug a 2 in for x and a 1 in for z, and we have 2 + y + 1 = 4, or 3 + y = 4, and subtracting 3 from both sides, y = 1. So x = 2, y = 1, and z = 1, and finally, we write our answer as the ordered triple, x, y, z, or (2, 1, 1).
Example 4: Adding and subtracting polynomials | Algebra I | Khan Academy
By Khan Academy
This video is from Khan Academy. It demonstrates the proper method of adding and subtracting polynomials
Composite Functions: f(g(x)) and g(f(x)) | MathHelp.com
By MathHelp.com
In this problem, we’re asked to add the given polynomials, then we’re asked to subtract the second polynomial from the first. In part a, to add the given polynomials, we simply add parentheses t^2 + 6t – 9 + parentheses t^2 + 7t - 3. Notice that I used parentheses around the polynomials. This is a good habit to get into, even though the parentheses will not affect the addition. Next, we simply add the like terms, t^2 + t^2 is 2t^2, 6t + 7t is 13t, and -9 - 3 is -12. So we have 2t^2 + 13t – 12. In part b, we’re asked to subtract the second polynomial from the first, so we have parentheses t^2 + 6t – 9 minus parentheses t^2 + 7t - 3. Notice that the second polynomial is subtracted from the first. And again, notice that we use parentheses around each polynomial. Now, it’s important to understand that the minus sign outside the second set of parentheses can be thought of as a negative 1, so we need to distribute the -1 through each of the terms in the second set of parentheses. So, after rewriting our first polynomial, t^2 + 6t – 9, we have -1 times t^2, or –t^2, -1 times positive 7t, which is -7t, and -1 times -3, which is positive 3. Now, we combine like terms. t^2 – t^2 cancels out, positive 6t minus 7t is -1t, or –t, and -9 + 3 is -6. So we have –t – 6. Makes sure to distribute the negative 1 through the parentheses when subtracting the second polynomial from the first.
16 - Add and Multiply Complex Numbers - Part 1
By Math and Science
Quality Math And Science Videos that feature step-by-step example problems!
18 - Dividing Complex Numbers - Part 1
By Math and Science
Quality Math And Science Videos that feature step-by-step example problems!
Area Between Two Curves
By The Organic Chemistry Tutor
This calculus video tutorial provides a basic introduction in finding the area between two curves with respect to y and with respect to x. It explains how to set up the definite integral to calculate the area of the shaded region bounded by the two curves. In order to find the points of intersection, you need to set the two curves equal to each other and solve for x or y. You need to be familiar with some basic integration techniques for this lesson. This video contains plenty of examples and practice problems.
ALL OF GRADE 9 MATH IN 60 MINUTES!!! (exam review part 1)
By Lumos Learning
Here is a great exam review video reviewing all of the main concepts you would have learned in the MPM1D grade 9 academic math course. The video is divided in to 3 parts. This is part 1: Algebra. The main topics in this section are exponent laws, polynomials, distributive property, and solving first degree equations. Please watch part 2 and 3 for a review of linear relations and geometry. If you watch all 3 parts, you will have reviewed all of grade 9 math in 60 minutes. Enjoy! Visit jensenmath.ca for more videos and course materials.
Functions and Graphs
By The Organic Chemistry Tutor
This precalculus provides a basic introduction into functions and graphs. It contains plenty of examples and multiple choice practice problems.
Rotational Dynamics - Basic Introduction
By The Organic Chemistry Tutor
This physics video tutorial provides a basic introduction into rotational dynamics. It explains how to calculate the acceleration of a hanging mass attached to a rotating pulley. Examples include pulleys with two hanging masses (atwood machine) and inclined planes with pulleys and kinetic friction.
Integration By Partial Fractions
By The Organic Chemistry Tutor
This calculus video tutorial provides a basic introduction into integrating rational functions using the partial fraction decomposition method. Partial fraction decomposition is the process of breaking a single complex fraction into multiple simpler fractions. The integrals of many rational functions lead to a natural log function with absolute value expressions. This video explains what to do when you have repeated linear factors and quadratic factors. This tutorial contains many examples and practice problems on integration by partial fractions.
Trigonometric Substitution
By The Organic Chemistry Tutor
This calculus video tutorial provides a basic introduction into trigonometric substitution. It explains when to substitute x with sin, cos, or sec. It also explains how to perform a change of variables using u-substitution integration techniques and how to use right triangle trigonometry with sohcahtoa to convert back from angles in the form of theta to an x variable. There's plenty of examples and practice problems in this lesson.
06 - Solve Quadratic Systems of Equations by Substitution - Part 1 (Simultaneous Equations)
By Math and Science
Quality Math And Science Videos that feature step-by-step example problems!
How To Integrate Using U-Substitution
By The Organic Chemistry Tutor
This calculus video tutorial provides a basic introduction into u-substitution. It explains how to integrate using u-substitution. You need to determine which part of the function to set equal to the u variable and you to find the derivative of u to get du and solve for dx. After replacing all x variables with u variables, find the antiderivative of f(u) and substitute u in the new function with x variables. This video contains plenty of examples and practice problems of finding the indefinite integral using u-substitution. Examples include polynomial functions, trigonometric functions, exponential functions, square root functions, and rational functions.
04 -What is an Arithmetic Sequence? - Part 1 - Arithmetic Sequence Formula & Examples
By Math and Science
Quality Math And Science Videos that feature step-by-step example problems!
