factoring A QUADRATIC TRINOMIAL MATH G99

QUADRATIC TRINOMIAL

2. GROUP ACTIVITY
An ANAGRAM is
a type of word play, the result
of
rearranging the letters of a word or phrase to
produce
a new word or phrase, using all the
original
letters exactly once.
Example  CARTHORSE  can
be rearranged into
ORCHESTRA.

3. Anagram of the word GRAB LEA
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ALGEBRA
0

4. Anagram of the word ACID QUART
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QUADRATIC
0

5. Anagram of the word PEN XEROSIS
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EXPRESSION
0

6. Anagram of the word ON A QUIET
EQUATION
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7. Anagram of the word ACTING FOR
FACTORING
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8. Anagram of the word MELTING COP
COMPLETING
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9. Anagram of the word FOUL ARM
FORMULA
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10. Anagram of the word ARDTANDS
STANDARD
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11. Anagram of the word UNFIT CON
FUNCTION
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12. Anagram of the word BEL PROM
PROBLEM
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13. Anagram of the word ARMS FRONT
TRANSFORM
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14. Anagram of the word OPEN NEXT
EXPONENT
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15. Anagram of the word PUT CORD
PRODUCT
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16. Anagram of the word LAY QUIET
EQUALITY
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17. 1. How are you going to deal
problems you encounter in life?
2. What techniques are you
going to use just to overcome
such problems?

18. Solving Roots/ Zeros of Simple
Quadratic Trinomial Equations
• FACTORING

19. Factors
Factors (either numbers or polynomials)
When an integer is written as a product of
integers, each of the integers in the product is a
factor of the original number.
When a polynomial is written as a product of
polynomials, each of the polynomials in the
product is a factor of the original polynomial.
Factoring – writing a polynomial as a product of
polynomials.

20. Solving Quadratic Equations
Steps for Solving a Quadratic Equation by
Factoring
1)Write the equation in standard form.
2)Factor the quadratic completely.
3)Set each factor containing a variable equal
to 0.
4)Solve the resulting equations.
5)Check each solution in the original
equation.

21. Factor
the polynomial
x
2

+ 13
x
+ 30.
Since our two numbers must have a product of 30 and
a sum of 13, the two numbers must both be positive.
Positive factors of 30Sum of Factors
1, 30 31
2, 15 17
3,
10
13
Note,
there are other factors, but once we find
a
pair that works, we do not have to continue
searching.
So

x
2

+ 13
x
+ 30 = (
x
+ 3)(
x
+ 10).
Factoring Polynomials
Example

22. Factor
the polynomial
x
2

– 2
x
– 35.
Since our two numbers must have a product of – 35 and a
sum of – 2, the two numbers will have to have different
signs.
Factors of – 35 Sum of Factors
– 1, 35 34
1, – 35 – 34
– 5, 7 2
5,

–

7 –

2
So

x
2

– 2
x
– 35 = (
x
+ 5)(
x
– 7).
Example

23. Factor
the polynomial
x
2

– 11
x
+ 24.
Since our two numbers must have a product of 24 and
a sum of -11, the two numbers must both be negative.
Negative factors of 24Sum of Factors
– 1, – 24 – 25
– 2, – 12 – 14
–

3,

–

8 –

11
So

x
2

– 11
x
+ 24 = (
x
– 3)(
x
– 8).
Example

24. Solve x
2
– 5x = 24.
•First write the quadratic equation in standard form.
x
2
– 5x – 24 = 0
•Now we factor the quadratic using techniques from
the previous steps.
x
2
– 5x – 24 = (x – 8)(x + 3) = 0
•We set each factor equal to 0.
x – 8 = 0 or x + 3 = 0, which will simplify to
x = 8 or x = – 3
Example
Continued.

25. •Check both possible answers in the original
equation.
8
2
– 5(8) = 64 – 40 = 24 true
(–3)
2
– 5(–3) = 9 – (–15) = 24 true
•So our solutions for x are 8 or –3.
Example Continued

26. Factoring allows us to solve
things. Sometimes, that is our
only way of being able to solve
something which is complicated.
You break down more complicate
object into simpler objects, such
that it is easier to explore their
structure or handle separately.

27. 1.Accuracy 10pts.
2.Neatness 5pts.

3.Group Attitude 5pts.
10 min11 min10 min9 min.8 min7 min6 min5 min4 min3 min2 min1 min100

29. Solve by Factoring:

30. 10 min11 min10 min9 min.8 min7 min6 min5 min4 min3 min2 min1 min100