Factor: 12x2 - 17x 6
Practice factoring a trinomial with a negative middle term: 12x2 - 17x 6.
Subject: sum
Transcript: 'LL MULTIPLY THE LEADING COEFFICIENT BY THE LAST TERM. 12 TIMES 6 IS 72. SO WE'LL HAVE TO FIND A PAIR OF NUMBERS WHOSE PRODUCT IS POSITIVE 72 AND WHOSE SUM IS
Solving Quadratic Equations by Factoring
A quadratic equation in which the quadratic trinomial has a leading coefficient of one can be solved by factoring. An example is given that also utilizes the zero factor property.
Subject: sum
Transcript: NUMBERS MUST HAVE A SUM THAT IS THE SAME AS THE COEFFICIENT OF THE MIDDLE TERM. THEY MUST ALSO HAVE A PRODUCT THAT IS THE SAME AS THE LAST TERM. SO WE NEED
Solving Equations Not Written in Standard Form
Before solving a quadratic equation, it must be written in standard form. The procedure is demonstrated.
Subject: sum
Transcript: 0 ON THE RIGHT, WE CAN FIND THE SOLUTION. FIRST WE'LL FACTOR THE TRINOMIAL. WE NEED TWO NUMBERS WHOSE SUM IS NEGATIVE 3 AND WHOSE PRODUCT IS NEGATIVE
Factor: 3c2 - 13cd 14d2
Practice factoring a trinomial with two different variables: 3c2 - 13cd 14d2.
Subject: sum
Transcript: THE COEFFICIENTS OF THE FIRST TERM AND THE LAST TERM. 3 TIMES 14 IS 42 WE ALSO WANT THE PAIR OF NUMBERS TO HAVE A SUM OF NEGATIVE 13. TO GET A POSITIVE
Factor: a2 12a 27
Demonstration of a shortcut that can be used to factor a quadratic trinomial with a leading coefficient of 1.
Subject: sum
Transcript: VARIABLE. THE CONSTANTS IN THE BINOMIAL FACTORS WILL BE THE PAIR OF NUMBERS THAT MEET TWO REQUIREMENTS, THEIR SUM MUST BE EQUAL TO THE MIDDLE TERM
Factor: 9y2 - 15y 4
Practice factoring a trinomial with a negative middle term: 9y2 - 15x 4.
Subject: sum
Transcript: 9 TIMES 4, OR 36. THE NUMBERS MUST ALSO HAVE A SUM OF NEGATIVE 15, SO WE'LL LOOK FOR TWO NEGATIVE NUMBERS. NEGATIVE 1 AND NEGATIVE 36 WON'T WORK
Factor: 8a2 10a 3
Practice factoring: 8a2 10a 3.
Subject: sum
Transcript: LET'S FACTOR THIS TRINOMIAL. WE'LL START BY LOOKING FOR TWO NUMBERS WHOSE SUM IS THE COEFFICIENT OF THE MIDDLE TERM, THAT'S 10. THE TWO NUMBERS MUST
Identities for Addition and Multiplication
Two important laws for solving equations are the identities for addition and multiplication.
Subject: sum
Identity for Addition
The identity for addition is zero. It works for all numbers and for the variables used in algebra.
Subject: sum
Transcript: NARRATOR: IF WE ADD 0 AND ANY OTHER NUMBER, THE SUM WILL BE THAT OTHER NUMBER. ADD 7 AND 0, YOU GET 7. NEGATIVE 5 AND 0, NEGATIVE 5. THE 0 CAN COME
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: sum
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