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: factor
Transcript: 8. SO WE'LL MULTIPLY EACH SIDE OF THE EQUATION BY THESE FACTORS. N THE LEFT SIDE, WE'LL BEGIN BY MULTIPLYING THEM BY 3/X. THE X'S CANCEL. THAT LEAVES
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: factor
Transcript: 'LL MULTIPLY BOTH SIDES OF THE EQUATION BY THESE FACTORS. FIRST, WE'LL MULTIPLY THE LEFT SIDE. THE LEAST COMMON DENOMINATOR TIMES 2 OVER X MINUS 3. THE X MINUS 3
Practical Problem: Machines Working at Different Speeds
The procedure for developing an equation to solve a practical work problem involving machines working at different speeds is detailed. The unknown is identified and an equation is written, solved, and checked.
Subject: factor
Transcript: FACTORS. WE'LL START ON THE LEFT SIDE. WHEN WE MULTIPLY THE LEAST COMMON DENOMINATOR BY 1/X, WE CANCEL THESE X'S. THEN WE HAVE 8 TIMES X MINUS 3. WHEN WE
Practical Problem: Runners' Rate of Speed
The rate, time, and distance formula is used to solve a practical problem involving runners' rate of speed.
Subject: factor
Transcript: LEAST COMMON DENOMINATOR IN THE EQUATION IS X TIMES X PLUS 3.1. SO WE'LL MULTIPLY BOTH SIDES OF THE EQUATION BY THESE FACTORS. WE'LL BEGIN WITH THE LEFT
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
Series: Factoring, Part Two
Subject: factor
Transcript: KEEP IN MIND THAT NOT ALL POLYNOMIALS CAN BE FACTORED. HERE'S ONE WHERE NO REARRANGING OR GROUPING WILL GIVE US COMMON FACTORS. WE CAN GROUP THE
Factor: y2 12y 32
Practice factoring: y2 12y 32.
Series: Factoring, Part Three
Subject: factor
Transcript: Y SQUARED PLUS 12Y PLUS 32. THE FACTORS ARE TWO BINOMIALS. THE FIRST TERM IN EACH BINOMIAL IS Y. THE CONSTANTS IN THE FACTORS WILL BE THE TWO
Terms Can Be Grouped Differently
There is often more than one way to group a polynomial expression for factoring. The commutative law can be applied to rearrange the terms into
Series: Factoring, Part Two
Subject: factor
Transcript: THERE'S OFTEN MORE THAN ONE WAY TO GROUP FACTORABLE POLYNOMIALS LIKE THIS. WE CAN GROUP THE FIRST TWO AND LAST TWO TERMS. BUT WE CAN ALSO USE THE
Factor: ax 3x 3b 3y
A polynomial with four terms can be factored by grouping when there is no factor common to all four terms. The procedure is demonstrated and the
Series: Factoring, Part Two
Subject: factor
Transcript: NOT ALL POLYNOMIALS CAN BE FACTORED INTO THE PRODUCT OF A GREATEST COMMON MONOMIAL FACTOR AND A POLYNOMIAL FACTOR. THE TERMS IN THIS POLYNOMIAL, FOR
Factor: d2 - 13d 30
The terms in a quadratic trinomial can be positive or negative. A quadratic trinomial in which the middle term is negative is factored.
Series: Factoring, Part Three
Subject: factor
Transcript: . NEGATIVE 3 AND NEGATIVE 10, HOWEVER, ADD UP TO NEGATIVE 13. AND THAT'S JUST WHAT WE WANT. NOW WE CAN USE THESE NUMBERS TO WRITE THE FACTORS. WE'LL HAVE TWO
Shortcut for Simplifying Radicals Before and After Multiplying
To avoid having to find perfect square factors for a large number by multiplying two radicals, first look for a common factor in the radicands that
Subject: factor
Transcript: THE SQUARE ROOT OF 27 TIMES THE SQUARE ROOT OF 15. IF WE MULTIPLY FIRST, WE'LL HAVE TO LOOK FOR PERFECT SQUARE FACTORS OF 405. THAT COULD TAKE A