Download Tremendous Trinomial technique

Take Out Something Common
(TOSC)
Look for the Greatest Common Factor for each of the terms in the polynomial.
Divide the coefficients.
Subtract the exponents.
3x2 + 6x
12x2y + 16xy3z
3 and 6 both divide by 3.
x2 and x both divide by x.
So the GCF is 3x.
Thus it factors into:
3x(x + 2)
12 and 16 both divide by 4.
x2 and x both divide by x.
y and y3 both divide by y and
nothing and a z means no z can be pulled out.
So the GCF is 4xy.
Thus it factors into:
4xy(3x + 4y2z)
Perfect Square Binomial
(PSB)
To recognize a Perfect Square Binomial:
1.
It must be a Binomial
2.
It must have a Perfect Square for each term
3.
It must be a subtraction
I.e., it looks like PS#1 – PS#2
It will always factor into:
(PS#1 + PS#2) (PS#1 - PS#2)
9x2 - 16
factors into
(3x + 4)(3x – 4)
81x2 – 144y6
factors into
(9x + 12y3)(9x – 12y3)
Perfect Square Trinomial
(PST)
To recognize a Perfect Square Trinomial:
1.
It must be a Trinomial
2.
It must have a Perfect Square for the first and last terms (PS#1 & PS#2)
3.
The last term must be positive
4.
The middle term must be the product of: 2*(PS#1 * PS#2)
I.e., it looks like PS#1 +/- [2*(PS#1 * PS#2)] + PS#2
It will always factor into:
(PS#1 + PS#2)2 OR (PS#1 - PS#2) 2
You will decide which one by the sign of the middle term.
9x2 + 12x + 4
factors into:
(3x+2)2
16x2 – 40x + 25
factors into:
(4x – 5) 2
Tremendous Trinomial Technique
(TTT)
6x2 + 17x + 7
what are the factors of 6 and 7?
1, 6 and 2, 3
and 1, 7
7 is positive so I either need 2 positive or 2 negative numbers.
According to the middle term it is 2 positives.
They must add up together to be 17
1*1 = 1
6*1=6
2*1 = 2
3*1 = 3
and
and
and
and
6*7 = 42
1*7=7
3 * 7 = 21
2 * 7 = 14
1+ 42 = 43
6+7 = 13
2 + 21 = 23
3+ 14 = 17
NOPE
NOPE
NOPE
YEP!!!
Now we have 3 and 14 for our new middle terms – they need to have an x attached to them to
become 3x and 14x. So I will re-write the problem replacing the middle term, 17x, with these 2
new terms….
6x2 + 3x + 14x + 7
Then I will divide the problem into 2 sections of TOSC.
6x2 + 3x + 14x + 7
Then I will do the factoring of TOSC to each half.
Remember that whatever is in the binomial quantity in the first half must also be in the second
binomial quantity!!!!
6x2 + 3x
+ 14x + 7
3x(2x + 1)
7(2x + 1)
Put the 3x and the 7 together to make a binomial.
Then use the 2x+1 binomial.
Then the final answer is:
(3x + 7)(2x + 1)
Quadratic Formula
This is your last chance to find a solution when the polynomial is equal to zero and none of the
factoring techniques work!
Biggest errors:
1.
Forgetting to put the OPPOSITE of b.
2.
Forgetting that it is the ENTIRE NUMERATOR divided by 2a.
3.
Forgetting to do both the addition AND subtraction
4.
Forgetting to simplify the radical term when possible.