Some Problems are More Easily Solved Using Two Variables
A practical problem is presented that demonstrates a situation in which two variables and a system of equations is the easiest way to reach a solution.
Subject: term
Transcript: 'S USE THE ELIMINATION METHOD TO ELIMINATE THE Y-TERMS. WE'LL MULTIPLY THE FIRST EQUATION BY 2 AND THE SECOND EQUATION BY NEGATIVE 3. NOW WE CAN ADD THE
Review of Techniques for Solving Systems of Equations
Review of techniques that can be used in solving systems of equations, including the elimination method and the substitution method.
Subject: term
Transcript: SYSTEM HAD NO VARIABLE TERMS THAT WERE ADDITIVE INVERSES, WE USE THE MULTIPLICATION PROPERTY OF EQUALITY. THAT'S THE PROPERTY THAT ALLOWS US TO MULTIPLY
Rules for Multiplying a Longer Expression by a Monomial and Rearranging Polynomials
Multiply a long expression by a monomial by working term-by-term, multiplying each term in the longer expression by the monomial.
Subject: term
Transcript: NARRATOR: TO MULTIPLY A LONGER EXPRESSION BY A MONOMIAL, WORK TERM BY TERM, MULTIPLYING EACH TERM IN THE LONGER EXPRESSION BY THE MONOMIAL. NOTICE
Practical Problem: Two Solutions for a Work Problem
A practical work problem that requires finding out how long it will take two workers with different work speeds to complete a task is solved using an equation with a rational expression. Two different approaches to finding the solution to this probl...
Subject: term
Transcript: SIDE OF THE EQUATION, 120X TIMES 1/X IS 120. NOW WE CAN COMBINE TERMS ON THE LEFT SIDE OF THE EQUATION. NEXT, DIVIDE BOTH SIDES OF THE EQUATION BY 8, X
Practical Problem: Two solutions for a Pool Problem
A work problem is presented to determine how long it will take to fill a pool that has an open drain.
Subject: term
Transcript: . MULTIPLY BY X AND WE HAVE 9X. NEXT, WE'LL MULTIPLY THE SECOND TERM. 576 DIVIDED BY 72 IS 8. MULTIPLY BY X AND WE GET 8X. N THE RIGHT SIDE OF THE EQUATION
Practical Problem: Wages of an Electrician and an Apprentice
Using the elimination method of calculate the hourly pay rates of an electrician and his apprentice on two different jobs given the total cost of each job.
Subject: term
Transcript: IN THE SYSTEM. NOW LET'S TAKE A LOOK AT THE TERMS IN THE EQUATIONS AND DECIDE HOW WE WANT TO SOLVE THIS SYSTEM. WE CAN ELIMINATE EITHER VARIABLE. WE
Recognizing Terms in an Expression
Identifying terms within an algebraic expression.
Subject: term
Transcript: NARRATOR: HERE'S AN ALGEBRAIC EXPRESSION. HOW MANY TERMS DOES IT HAVE? THERE ARE THREE TERMS: 8AB SQUARED, 9AC, AND 4. NOTICE THAT EVEN THOUGH THE 4
Factoring Problems
Factoring polynomials using three examples to practice procedures and techniques. Be sure the polynomial has been simplified before factoring. Remember that some expressions are not factorable.
Subject: term
Transcript: TRY FACTORING THIS POLYNOMIAL. PAY ATTENTION TO THE TERMS AND THE EXPONENTS HERE. REMEMBER, BEFORE WE FACTOR, WE MUST BE SURE THAT THE POLYNOMIAL
Factoring by Inspection
Sometimes the greatest common factor is immediately recognizable. Definition and demonstration of factoring by inspection.
Subject: term
Transcript: GREATEST COMMON FACTOR? IT'S 9X. 9 AND X ARE FACTORS OF BOTH TERMS. WHEN 9X IS FACTORED FROM 9XZ MINUS 9XY, WE'RE LEFT WITH THE OTHER FACTOR, Z MINUS Y. WE
Factoring with (-1) to Rewrite a Polynomial
Factoring with negative numbers. Using negative one to change the signs of each term in an expression.
Subject: term
Transcript: WE CAN FACTOR WITH NEGATIVE NUMBERS. FOR EXAMPLE, WE MAY WANT TO FACTOR WITH NEGATIVE 1 TO CHANGE THE SIGNS OF EACH TERM IN AN EXPRESSION. SUPPOSE