More About Using Least Common Multiples
The least common multiple strategy reveals a system of equations that has not solution.
Subject: term
Transcript: NARRATOR: HERE'S ANOTHER SYSTEM WE CAN SOLVE USING THE LEAST COMMON MULTIPLE. LOOK AT THE VARIABLE TERMS. WE'LL ELIMINATE X. LET'S FIND THE LEAST
Practical Problem: Finding the Speed of the Wind
A practical problem involving two airplanes requires finding their true speed after factoring in wind speed. The rate, time, and distance formula is used to solve the problem.
Subject: term
Factor: b2 9b 20
A quadratic trinomial with a leading coefficient of 1 is factored, producing a four-term polynomial. The factor is then checked by multiplying using
Subject: term
Transcript: SUM OF THOSE TWO NUMBERS AND THE PRODUCT OF THOSE NUMBERS. THE NUMBERS MUST ADD UP TO THE COEFFICIENT OF THE MIDDLE TERM. THAT'S 9. THE NUMBERS MUST
Solving a System Using the Same Variable
Practice solving a system of equations with the same variable.
Subject: term
Transcript: NARRATOR: HERE'S ANOTHER SYSTEM TO SOLVE. ITS SOLUTION WILL BE THE VALUES FOR THE ORDERED PAIR A, B. LOOK AT THE TERMS IN BOTH EQUATIONS. EACH ONE
Introduction to Factoring Quadratic Trinomials
A quadratic trinomial is a polynomial with three terms. In two of the terms the same variable appears, one that is raised to the second power and the
Subject: term
Transcript: . QUADRATIC TRINOMIALS HAVE THREE TERMS. THE SAME VARIABLE APPEARS IN TWO TERMS. IN ONE OF THE TERMS, THE VARIABLE IS RAISED TO THE SECOND POWER. IT'S SQUARED
Factor: 2k2 - 18k - 72
Factoring a quadratic trinomial with a leading coefficient greater than one.
Subject: term
Transcript: NEGATIVE 12 HAVE A SUM OF NEGATIVE 9. THAT'S IT. NOW WE CAN FACTOR. 2 IS THE GREATEST COMMON FACTOR. THE OTHER FACTORS ARE TWO BINOMIALS. THE FIRST TERM OF
Not All Quadratic Trinomials Can Be Factored
A quadratic trinomial that cannot be factored is presented and explained.
Subject: term
Multiplying by the Least Common Denominator to Get a Quadratic Equation
The steps involved in solving an equation by multiplying by the least common denominator to get a quadratic equation and checking the solution are detailed.
Subject: term
Transcript: COMBINE TERMS. THIS IS A QUADRATIC EQUATION. WE CAN SOLVE IT BY FACTORING OR BY USING THE QUADRATIC FORMULA. BUT TO USE EITHER OF THESE METHODS, WE'LL HAVE
Solving an Equation with the Least Common Denominator: Practice Problem
A problem is presented to practice solving an equation using the least common denominator to get a quadratic equation.
Subject: term
Transcript: , WE'LL SIMPLIFY THE TERMS IN THE EQUATION. THE FIRST TERM EQUALS 18X MINUS 72. THE SECOND TERM EQUALS 27X MINUS 81. THE RIGHT SIDE OF THE EQUATION
Some Polynomials Cannot be Factored
Sometimes there is no way to rearrange or group that produces common factors. A polynomial that cannot be factored down to one term is said to be
Subject: term
Transcript: FIRST TWO TERMS AND THE LAST TWO TERMS. FACTORING THESE GROUPS GIVES US 3 TIMES THE QUANTITY X PLUS Z PLUS 2 TIMES THE QUANTITY W PLUS Y. THESE TWO TERMS