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: sum
Introduction to Factoring Quadratic Trinomials
terms to create a four-term polynomial that can be factored by grouping. To expand the middle term, two numbers must be found that have a sum equal to the
Subject: sum
Transcript: MIDDLE TERM OF THE TRINOMIAL AS THE SUM OF TWO TERMS. THAT'LL GIVE US A FOUR-TERM POLYNOMIAL, WHICH WE CAN FACTOR BY GROUPING. BUT BEFORE WE CAN FACTOR
Factor: 2k2 - 18k - 72
Factoring a quadratic trinomial with a leading coefficient greater than one.
Subject: sum
Transcript: OF NUMBERS WHOSE PRODUCT IS NEGATIVE 36 AND WHOSE SUM IS NEGATIVE 9. TO GET A NEGATIVE PRODUCT, WE NEED ONE POSITIVE NUMBER AND ONE NEGATIVE NUMBER. WE
Not All Quadratic Trinomials Can Be Factored
A quadratic trinomial that cannot be factored is presented and explained.
Subject: sum
Transcript: NOT ALL QUADRATIC TRINOMIALS CAN BE FACTORED. LOOK AT THIS ONE. IN ORDER TO FACTOR IT, WE NEED TO FIND TWO NUMBERS WHOSE PRODUCT IS 12 AND WHOSE SUM
Factor: y2 12y 32
Practice factoring: y2 12y 32.
Subject: sum
Transcript: NUMBERS WHOSE PRODUCT EQUALS 32 AND WHOSE SUM EQUALS 12. 1 AND 32 WON'T WORK. 2 AND 16 ARE FACTORS OF 32, BUT THEY HAVE A SUM OF 18. 4 AND 8 HAVE A PRODUCT
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.
Subject: sum
Transcript: OF NUMBERS THAT HAS A SUM OF NEGATIVE 13. THE PAIR OF NUMBERS MUST ALSO HAVE A PRODUCT OF POSITIVE 30. SO WE WANT TWO NUMBERS THAT GIVE US A POSITIVE
Factor: x2 5xy 4y2
Factoring a trinomial with two different variables: x2 5xy 4y2.
Subject: sum
Transcript: THE KEY TO FACTORING QUADRATIC TRINOMIALS IS FINDING A PAIR OF NUMBERS THAT HAS A CERTAIN PRODUCT AND A CERTAIN SUM. THAT'S ALSO THE KEY TO
Factor: 3x2 14x 8
quadratic trinomial with a coefficient greater than one look for a pair of numbers in which the sum is equal to the coefficient of the middle term and whose
Subject: sum
Transcript: . THEIR SUM IS 14, THE SAME AS THE COEFFICIENT OF THE MIDDLE TERM. BUT WHAT ABOUT THE PRODUCT OF THE TWO NUMBERS? 2 TIMES 12 IS 24. THAT'S NOT THE SAME AS
Solve: m2 7m 12 = 0
Practice solving a quadratic equation: m2 7m 12 = 0.
Subject: sum
Transcript: FACTORS, WE'LL LOOK FOR TWO NUMBERS WHOSE SUM EQUALS 7 AND WHOSE PRODUCT EQUALS 12. LET'S THINK ABOUT THAT. 3 AND 4 WORK. SO THE BINOMIAL FACTORS ARE M PLUS
Factor: 8x2 10x - 25
Practice factoring a trinomial in which the last term is negative: 8x2 10x - 25.
Subject: sum
Transcript: HERE'S ANOTHER TRINOMIAL WITH A NEGATIVE TERM. THIS TIME THE LAST TERM IS NEGATIVE. WE NEED A PAIR OF NUMBERS WHOSE SUM IS 10. THE NUMBERS MUST ALSO