January 29, 2016
Lesson 6.2
Factoring x2 + bx + c
Consider
Therefore, the product of p and q equals c,
and the sum of p and q equals b..
Another way to state this is that we
must find factors of c whose sum is b.
What are the factors of 4?
Factors: 2 x 2 and 4 x 1
Sum: 2 + 2 = 4; 4 + 1 = 5
4
1
What other answer is also correct?
1
4
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January 29, 2016
Factor
What are we looking for?
We must find
d factors of 12 whose sum is 7.
4
3
What changes when we factor
Now we must find
d factors of 12 whose sum is -7.
4
3
What do we need to find in order to factor
Find factors of -6 whose sum is -1.
2
3
4
9
Factor each trinomial.
Find factors of -36 whose sum is -5.
3
14
Find factors of -42 whose sum is 11.
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January 29, 2016
What do you notice when you compare the
following trinomials?
They have opposite constant terms and different
coefficients for the x (linear) term.
Factor each.
1)
- 11
- 15
What must be true about the factors of 165
for this problem? They are both be negative.
a)
c)
b)
2)
d)
+ 15
- 11
What must be true about the factors of 165
for this problem? One is positive, one negative.
a)
c)
b)
d)
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January 29, 2016
Sometimes we have to factor out a GCF before we
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have a polynomial of the form x + bx + c.
Factor
How can we check our answer?
Check our answer!
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January 29, 2016
Make your own problem. Find all numbers
for b so that the following trinomial can be
factored.
-48 and 1; b = -47
-1 and 48; b = 47
-12 and 4; b = -8
12 and -4; b = 8
-6 and 8; b = 2
6 and -8; b = -2
-24 and 2; b = -22
24 and -2; b = 22
-3 and 16; b = 13
3 and -16; b = -13
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January 29, 2016
Make your own problem. Find all natural
numbers for c so that the following trinomial
can be factored.
1 + 10 = 11
2 + 9 = 11
3 + 8 = 11
4 + 7 = 11
5 + 6 = 11
c = 10
c = 18
c = 24
c = 28
c = 30
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January 29, 2016
Lesson 6.2 pages 430-431 even answers.
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January 29, 2016
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