Solving the Same Word Problem Using One and Two Variables
Three different approaches to solving the same practical problem are demonstrated. Two approaches using one variable and a two-variable system all produce the same solution to the question of how many balcony seats and how many floor seats can be so...
Subject: term
Transcript: THAN BALCONY SEATS. WHEN X IS THE NUMBER OF BALCONY SEATS, THE NUMBER OF FLOOR SEATS IS X PLUS 70. WE'VE DEFINED THE NUMBER OF FLOOR SEATS IN TERMS OF
Thoroughly Check for Common Factors
Be thorough when checking for common factors, especially when factoring by inspection. You have not factored completely until no common factors remain.
Subject: term
Transcript: COMMON FACTOR YOU SEE IS NOT THE GREATEST COMMON FACTOR. THIS POLYNOMIAL IS A GOOD EXAMPLE. SUPPOSE THAT AFTER QUICKLY INSPECTING THE TERMS, WE NOTICE THAT
Summary of the Addition of Like Terms
Review and practice of adding terms in a simple algebraic expression.
Subject: term
Transcript: NARRATOR: TO ADD TWO OR MORE TERMS, FIRST, SEE IF THEY ARE LIKE TERMS. IF NOT, JUST COPY THEM OVER. THERE IS NOTHING MORE YOU CAN DO. IF YOU FIND
Factoring Polynomials - The Distributive Law
Factoring is the process of writing a polynomial as a product of its factors. The distributive law is one of a number of ways to factor polynomials.
Subject: term
Transcript: POLYNOMIALS ARE ALGEBRAIC EXPRESSION WHERE TERMS ARE ADDED OR SUBTRACTED. EACH INDIVIDUAL TERM MAY INCLUDE ADDITION, SUBTRACTION, MULTIPLICATION, OR
Solving Equations That Include Rational Expressions
To solve an equation with a rational expression, rewrite the equation to get rid of the fractions then solve the new equation. The same process is used to solve linear equations that contain rational expressions. If the solution makes any denominato...
Subject: term
Transcript: TERMS ON THE LEFT SIDE OF THE EQUATION. TO DO THAT, WE'LL HAVE TO CHANGE 3/4 TO 9/12. NOW WE CAN ADD 5/12. WE GET 14/12. THAT REDUCES TO 7/6. THAT'S THE
Rewriting Equations in Order to Use the Elimination Method
Using the elimination method to solve a system of equations will sometimes require rewriting one of the equations.
Subject: term
Transcript: NARRATOR: HERE'S ANOTHER SYSTEM TO SOLVE. LOOK AT THE TERMS IN THE EQUATIONS AND THE FORM OF THE EQUATION. 6X AND NEGATIVE 6X ARE ADDITIVE INVERSES
Practical Problem: How Long it Will Take to do Payroll
A work problem requires finding out how long it will take two workers with different work speeds to complete a task. The process of developing an equation and solving it are detailed.
Subject: term
Factor: 3c2 - 13cd 14d2
Practice factoring a trinomial with two different variables: 3c2 - 13cd 14d2.
Subject: term
Transcript: COEFFICIENT GREATER THAN 1. WE'LL LOOK FOR A PAIR OF NUMBERS TO EXPAND THE MIDDLE TERM, THEN WE'LL FACTOR BY GROUPING. WE'LL START BY LOOKING FOR THE PRODUCT OF
Factor: 5y2 6y 5xy 6x
Practice factoring: 5y2 6y 5xy 6x.
Subject: term
Transcript: TRY FACTORING THIS POLYNOMIAL YOURSELF. INSPECT THE TERMS CAREFULLY BEFORE YOU GROUP THEM. WE CAN GROUP THE FIRST TWO TERMS AND THE LAST TWO TERMS
Factor: a2 12a 27
Demonstration of a shortcut that can be used to factor a quadratic trinomial with a leading coefficient of 1.
Subject: term
Transcript: WHEN WE FACTOR QUADRATIC TRINOMIALS WITH A LEADING COEFFICIENT OF 1, WE CAN TAKE A SHORTCUT. THE FIRST TERM IN EACH BINOMIAL FACTOR WILL BE THE