Factor: 3c2 - 13cd 14d2
Practice factoring a trinomial with two different variables: 3c2 - 13cd 14d2.
Subject: product
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: a2 12a 27
Demonstration of a shortcut that can be used to factor a quadratic trinomial with a leading coefficient of 1.
Subject: product
Transcript: 'S COEFFICIENT AND THEIR PRODUCT MUST BE EQUAL TO THE LAST TERM. SO ONCE WE FIND THE CORRECT PAIR OF NUMBERS, WE CAN SKIP GROUPING AND WRITE DOWN THE NUMBERS IN
Factor: 9y2 - 15y 4
Practice factoring a trinomial with a negative middle term: 9y2 - 15x 4.
Subject: product
Transcript: HERE'S ANOTHER TRINOMIAL WITH A NEGATIVE MIDDLE TERM. WE'LL BE CAREFUL WITH SIGNS AS WE FACTOR BY GROUPING. WE WANT TWO NUMBERS WHOSE PRODUCT EQUALS
Factor: 8a2 10a 3
Practice factoring: 8a2 10a 3.
Subject: product
Transcript: ALSO HAVE A PRODUCT THAT'S EQUAL TO THE LEADING COEFFICIENT MULTIPLIED BY THE LAST TERM, THAT'S 8 TIMES 3, OR 24. 1 AND 24 HAVE A PRODUCT OF 24, BUT A
Simplifying Radicals Using Multiplication
Radicals are simplified using multiplication, illustrating when to multiply first and then find the square root of the product and when to find the
Subject: product
Transcript: FIND THE SQUARE ROOTS FIRST, THEN MULTIPLY. OR WE CAN MULTIPLY FIRST, THEN FIND THE SQUARE ROOT OF THE PRODUCT. IN THIS PROBLEM, WE COULD GO EITHER WAY
Identify for Multiplication
The identity for multiplication is one. It applies to all numbers and to algebraic variables and expressions.
Subject: product
Transcript: COMES FIRST OR SECOND. EITHER WAY, THE PRODUCT IS IDENTICAL TO THE OTHER NUMBER. THE LAW SAYS THAT IF WE MULTIPLY 1 BY ANY OTHER NUMBER, THE PRODUCT WILL
Factoring before Multiplying Rational Expressions
If a rational expression is more complicated, factoring before multiplying might be indicated.
Subject: product
Transcript: CANCELED, IN SIMPLEST FORM, THE PRODUCT OF THESE TWO RATIONAL EXPRESSIONS IS N MINUS 4. HERE'S ANOTHER MULTIPLICATION PROBLEM. THIS IS ANOTHER CASE IN WHICH
Factoring Review
A review of factoring of numbers and polynomials.
Subject: product
Transcript: WHEN WE FACTORED NUMBERS, WE STARTED WITH A NUMBER CALLED A PRODUCT. THEN WE FOUND ITS FACTORS, THE NUMBERS WE COULD MULTIPLY TO FIND THE PRODUCT
Practical Problem: Expanding a Parking Lot
Using a quadratic equation to solve a practical problem involving enlarging a parking lot. Checking the solution to be sure it makes sense in the context of the problem.
Subject: product
Transcript: PRODUCT IS NEGATIVE 5,400 AND WHOSE SUM IS 150. THE NUMBERS ARE NEGATIVE 30 AND POSITIVE 180. THE FACTORS ARE X MINUS 30 AND X PLUS 180. NOW LET EACH FACTOR
Practical Problem: The Path of a Golf Ball
Using a quadratic equation to describe the relationship between variables in a practical problem involving the flight time of a golf ball.
Subject: product